Recent Advances In Alexandrov Geometry

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Recent Advances in Alexandrov Geometry

Gerardo Arizmendi Echegaray,Luis Hernández-Lamoneda,Rafael Herrera Guzmán
Recent Advances in Alexandrov Geometry Book PDF

Author : Gerardo Arizmendi Echegaray,Luis Hernández-Lamoneda,Rafael Herrera Guzmán
Publisher : Springer Nature
Page : 119 pages
File Size : 44,6 Mb
Release : 2022-10-27
Category : Mathematics
ISBN : 9783030992989

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Recent Advances in Alexandrov Geometry by Gerardo Arizmendi Echegaray,Luis Hernández-Lamoneda,Rafael Herrera Guzmán Pdf

This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen’s part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs. The text from Fernando Galaz-García’s minicourse was completed in collaboration with Jesús Nuñez-Zimbrón. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces. Jesús Nuñez-Zimbrón’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.

Recent Advances in Geometric Analysis

Yng-Ing Lee,Chang-Shou Lin,Mao-Pei Tsui
Recent Advances in Geometric Analysis Book PDF

Author : Yng-Ing Lee,Chang-Shou Lin,Mao-Pei Tsui
Publisher : International Press of Boston
Page : 0 pages
File Size : 42,8 Mb
Release : 2010
Category : Geometric analysis
ISBN : 1571461434

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Recent Advances in Geometric Analysis by Yng-Ing Lee,Chang-Shou Lin,Mao-Pei Tsui Pdf

Explores recent advances in geometric analysis and related topics, including Ricci flow, affine normal flow, geometric analysis on pseudo-convex hypersurfaces, Alexandrov space, manifolds with special holonomy, and the singular plateau problem. It is intended for both researchers and graduate students studying geometric analysis and related areas.

A.D. Alexandrov

S.S. Kutateladze
A D Alexandrov Book PDF

Author : S.S. Kutateladze
Publisher : Chapman and Hall/CRC
Page : 440 pages
File Size : 42,9 Mb
Release : 2005-07-25
Category : Mathematics
ISBN : 1134429029

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A.D. Alexandrov by S.S. Kutateladze Pdf

A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results relevant to intrinsic geometry. It reviews the general theory, then presents the requisite general theorems on rectifiable curves and curves of minimum length. Proof of some of the general properties of the intrinsic metric of convex surfaces follows. The study then splits into two almost independent lines: further exploration of the intrinsic geometry of convex surfaces and proof of the existence of a surface with a given metric. The final chapter reviews the generalization of the whole theory to convex surfaces in the Lobachevskii space and in the spherical space, concluding with an outline of the theory of nonconvex surfaces. Alexandrov's work was both original and extremely influential. This book gave rise to studying surfaces "in the large," rejecting the limitations of smoothness, and reviving the style of Euclid. Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope.

Recent Advances in Riemannian and Lorentzian Geometries

Krishan L. Duggal,Ramesh Sharma
Recent Advances in Riemannian and Lorentzian Geometries Book PDF

Author : Krishan L. Duggal,Ramesh Sharma
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 54,9 Mb
Release : 2003
Category : Geometry, Differential
ISBN : 9780821833797

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Recent Advances in Riemannian and Lorentzian Geometries by Krishan L. Duggal,Ramesh Sharma Pdf

This volume covers material presented by invited speakers at the AMS special session on Riemannian and Lorentzian geometries held at the annual Joint Mathematics Meetings in Baltimore. Topics covered include classification of curvature-related operators, curvature-homogeneous Einstein 4-manifolds, linear stability/instability singularity and hyperbolic operators of spacetimes, spectral geometry of holomorphic manifolds, cut loci of nilpotent Lie groups, conformal geometry of almost Hermitian manifolds, and also submanifolds of complex and contact spaces. This volume can serve as a good reference source and provide indications for further research. It is suitable for graduate students and research mathematicians interested in differential geometry.

An Invitation to Alexandrov Geometry

Stephanie Alexander,Vitali Kapovitch,Anton Petrunin
An Invitation to Alexandrov Geometry Book PDF

Author : Stephanie Alexander,Vitali Kapovitch,Anton Petrunin
Publisher : Springer
Page : 88 pages
File Size : 48,9 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9783030053123

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An Invitation to Alexandrov Geometry by Stephanie Alexander,Vitali Kapovitch,Anton Petrunin Pdf

Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.

Recent Developments in Pseudo-Riemannian Geometry

Dmitriĭ Vladimirovich Alekseevskiĭ
Recent Developments in Pseudo Riemannian Geometry Book PDF

Author : Dmitriĭ Vladimirovich Alekseevskiĭ
Publisher : European Mathematical Society
Page : 556 pages
File Size : 55,6 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190515

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Recent Developments in Pseudo-Riemannian Geometry by Dmitriĭ Vladimirovich Alekseevskiĭ Pdf

This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.

Differential Geometry, Valencia 2001

Olga Gil-Medrano,Vicente Miquel,Antonio Mart¡nez Naveira
Differential Geometry Valencia 2001 Book PDF

Author : Olga Gil-Medrano,Vicente Miquel,Antonio Mart¡nez Naveira
Publisher : World Scientific
Page : 324 pages
File Size : 49,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9789810249069

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Differential Geometry, Valencia 2001 by Olga Gil-Medrano,Vicente Miquel,Antonio Mart¡nez Naveira Pdf

This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira. The meeting brought together distinguished researchers from a variety of areas in Riemannian geometry. The topics include: geometry of the curvature tensor, variational problems for geometric functionals such as Willmore-Chen tension, volume and energy of foliations and vector fields, and energy of maps. Many papers concern special submanifolds in Riemannian and Lorentzian manifolds, such as those with constant mean (scalar, Gauss, etc.) curvature and those with finite total curvature.

Differential Geometry, Valencia 2001

Olga Gil-Medrano,Vicente Miquel
Differential Geometry Valencia 2001 Book PDF

Author : Olga Gil-Medrano,Vicente Miquel
Publisher : World Scientific
Page : 324 pages
File Size : 49,8 Mb
Release : 2002-07-18
Category : Geometry, Differential
ISBN : 9789814488914

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Differential Geometry, Valencia 2001 by Olga Gil-Medrano,Vicente Miquel Pdf

This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira. The meeting brought together distinguished researchers from a variety of areas in Riemannian geometry. The topics include: geometry of the curvature tensor, variational problems for geometric functionals such as Willmore–Chen tension, volume and energy of foliations and vector fields, and energy of maps. Many papers concern special submanifolds in Riemannian and Lorentzian manifolds, such as those with constant mean (scalar, Gauss, etc.) curvature and those with finite total curvature. Contents: Hypersurfaces with Constant Higher Order Mean Curvature in Euclidean Space (L J Alías & J M Malacarne)Uniqueness of Spacelike Hypersurfaces with Constant Mean Curvature in Generalized Robertson–Walker Spacetimes (L J Alías & S Montiel)Critical Points of Willmore–Chen Tension Functionals (M Barros)Some Generalizations of Twistor Spaces (D E Blair)The Intrinsic Torsion of SU(3) and G2 Structures (S Chiossi & S Salamon)H-Hypersurfaces with Finite Total Curvature (M P do Carmo)Volume and Energy of Vector Fields on Spheres. A Survey (O Gil-Medrano)Spacelike Jordan Osserman Algebraic Curvature Tensors in the Higher Signature Setting (P B Gilkey & R Ivanova)The Gauss Map of Minimal Surfaces (A Ros)On Minimal Growth in Group Theory and Riemannian Geometry (A Sambusetti)Deformation of Lipschitz Riemannian Metrics in the Direction of their Ricci Curvature (M Simon)and other papers Readership: Graduate students and researchers in differential geometry. Keywords:

Recent Advances in Parallel Virtual Machine and Message Passing Interface

Vassil Alexandrov
Recent Advances in Parallel Virtual Machine and Message Passing Interface Book PDF

Author : Vassil Alexandrov
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 43,5 Mb
Release : 1998-08-26
Category : Computers
ISBN : 3540650415

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Recent Advances in Parallel Virtual Machine and Message Passing Interface by Vassil Alexandrov Pdf

This book constitutes the refereed proceedings of the 5th European Meeting of the Parallel Virtual Machine and Message Passing Interface Users' Group, PVM/MPI '98, held in Liverpool, UK, in September 1998. The 49 contributed and invited papers presented were carefully reviewed and revised for inclusion in the volume. All current aspects of PVM and MPI are addressed. The papers are organized in topical sections on evaluation and performance, extensions and improvements, implementation issues, tools, and algorithms.

A. D. Alexandrov Selected Works

Yu. G. Reshetnyak,S.S. Kutateladze
A D Alexandrov Selected Works Book PDF

Author : Yu. G. Reshetnyak,S.S. Kutateladze
Publisher : CRC Press
Page : 336 pages
File Size : 48,7 Mb
Release : 2002-02-21
Category : Mathematics
ISBN : 2881249841

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A. D. Alexandrov Selected Works by Yu. G. Reshetnyak,S.S. Kutateladze Pdf

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.

Noncompact Problems at the Intersection of Geometry, Analysis, and Topology

Noncompact Va Brezis-Browder Conference,Brezis-Browder Conference, Noncompact Variational Problems and General Relativity,Abbas Bahri,Sergiu Klainerman,Michael Vogelius
Noncompact Problems at the Intersection of Geometry Analysis and Topology Book PDF

Author : Noncompact Va Brezis-Browder Conference,Brezis-Browder Conference, Noncompact Variational Problems and General Relativity,Abbas Bahri,Sergiu Klainerman,Michael Vogelius
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 54,5 Mb
Release : 2004
Category : Science
ISBN : 9780821836354

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Noncompact Problems at the Intersection of Geometry, Analysis, and Topology by Noncompact Va Brezis-Browder Conference,Brezis-Browder Conference, Noncompact Variational Problems and General Relativity,Abbas Bahri,Sergiu Klainerman,Michael Vogelius Pdf

This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.

Geometric Control Theory and Sub-Riemannian Geometry

Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti
Geometric Control Theory and Sub Riemannian Geometry Book PDF

Author : Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti
Publisher : Springer
Page : 385 pages
File Size : 52,5 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9783319021324

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Geometric Control Theory and Sub-Riemannian Geometry by Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti Pdf

Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.

A. D. Alexandrov Selected Works

Yu G Reshetnyak
A D Alexandrov Selected Works Book PDF

Author : Yu G Reshetnyak
Publisher : CRC Press
Page : 332 pages
File Size : 52,6 Mb
Release : 2019-08-30
Category : Geometry
ISBN : 0367396319

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A. D. Alexandrov Selected Works by Yu G Reshetnyak Pdf

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.

Advances in Complex Geometry

Yanir A. Rubinstein,Bernard Shiffman
Advances in Complex Geometry Book PDF

Author : Yanir A. Rubinstein,Bernard Shiffman
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 49,8 Mb
Release : 2019-08-26
Category : Geometry
ISBN : 9781470443337

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Advances in Complex Geometry by Yanir A. Rubinstein,Bernard Shiffman Pdf

This volume contains contributions from speakers at the 2015–2018 joint Johns Hopkins University and University of Maryland Complex Geometry Seminar. It begins with a survey article on recent developments in pluripotential theory and its applications to Kähler–Einstein metrics and continues with articles devoted to various aspects of the theory of complex manifolds and functions on such manifolds.

Recent Advances in Parallel Virtual Machine and Message Passing Interface

Jack Dongarra,Emilio Luque,Tomas Margalef
Recent Advances in Parallel Virtual Machine and Message Passing Interface Book PDF

Author : Jack Dongarra,Emilio Luque,Tomas Margalef
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 50,6 Mb
Release : 1999-09-15
Category : Computers
ISBN : 9783540665496

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Recent Advances in Parallel Virtual Machine and Message Passing Interface by Jack Dongarra,Emilio Luque,Tomas Margalef Pdf

This book constitutes the refereed proceedings of the 6th European Meeting of the Parallel Virtual Machine and Message Passing Interface Users' Group, PVM/MPI '99, held in Barcelona, Spain in September 1999. The 67 revised papers presented were carefully reviewed and selected from a large number of submissions. All current issues of PVM and MPI are addressed. The papers are organized in topical sections on evaluation and performance, extensions and improvements, implementation issues, tools, algorithms, applications in science and engineering, networking, and heterogeneous distributed systems.