Real Methods In Complex And Cr Geometry

Author : Marco Abate,John Erik Fornaess,Xiaojun Huang,Jean-Pierre Rosay,Alexander Tumanov
Publisher : Springer
Page : 219 pages
File Size : 41,9 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9783540444879

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Real Methods in Complex and CR Geometry by Marco Abate,John Erik Fornaess,Xiaojun Huang,Jean-Pierre Rosay,Alexander Tumanov Pdf

The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.

Author : John Erik Fornaess,Xiaojun Huang,Jean-Pierre Rosay,Alexander Tumanov
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 55,6 Mb
Release : 2004
Category : CR submanifolds
ISBN : 3540223584

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Real Methods in Complex and CR Geometry by John Erik Fornaess,Xiaojun Huang,Jean-Pierre Rosay,Alexander Tumanov Pdf

Author : Giuseppe Zampieri
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 41,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821844427

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Complex Analysis and CR Geometry by Giuseppe Zampieri Pdf

Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the $\bar\partial$-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometryrequires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting tograduate students who wish to learn it.

Author : W. Weil,A. Baddeley,I. Bárány,R. Schneider
Publisher : Springer
Page : 302 pages
File Size : 44,5 Mb
Release : 2006-10-26
Category : Mathematics
ISBN : 9783540381754

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Stochastic Geometry by W. Weil,A. Baddeley,I. Bárány,R. Schneider Pdf

Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer
Page : 364 pages
File Size : 43,9 Mb
Release : 2003-12-15
Category : Mathematics
ISBN : 9783540397021

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 51,5 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783540798132

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Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Author : Ben Andrews,Christopher Hopper
Publisher : Springer
Page : 302 pages
File Size : 51,6 Mb
Release : 2010-11-09
Category : Mathematics
ISBN : 9783642162862

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The Ricci Flow in Riemannian Geometry by Ben Andrews,Christopher Hopper Pdf

This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.

Author : Christian Rohde
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 49,6 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783642006388

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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication by Christian Rohde Pdf

The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.

Author : Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin
Publisher : Springer
Page : 360 pages
File Size : 55,8 Mb
Release : 2008-06-24
Category : Science
ISBN : 9783540776536

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Nonlinear and Optimal Control Theory by Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin Pdf

The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.

Author : Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco
Publisher : Springer
Page : 213 pages
File Size : 48,5 Mb
Release : 2007-12-10
Category : Mathematics
ISBN : 9783540759140

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Calculus of Variations and Nonlinear Partial Differential Equations by Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco Pdf

This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

Author : Alberto Bressan,Denis Serre,Mark Williams,Kevin Zumbrun
Publisher : Springer
Page : 365 pages
File Size : 43,7 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540721871

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Hyperbolic Systems of Balance Laws by Alberto Bressan,Denis Serre,Mark Williams,Kevin Zumbrun Pdf

This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building blocks of the theory. Serre focuses on existence and stability for discrete shock profiles. The lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.

Author : J. B. Friedlander,D.R. Heath-Brown,H. Iwaniec,J. Kaczorowski
Publisher : Springer
Page : 217 pages
File Size : 42,5 Mb
Release : 2006-11-10
Category : Mathematics
ISBN : 9783540363644

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Analytic Number Theory by J. B. Friedlander,D.R. Heath-Brown,H. Iwaniec,J. Kaczorowski Pdf

The four papers collected in this book discuss advanced results in analytic number theory, including recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials; counting integer solutions to Diophantine equations, using results from algebraic geometry and the geometry of numbers; the theory of Siegel’s zeros and of exceptional characters of L-functions; and an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg.

Author : Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 44,6 Mb
Release : 2008-04-14
Category : Mathematics
ISBN : 9783540783145

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Mixed Finite Elements, Compatibility Conditions, and Applications by Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin Pdf

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Author : Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft
Publisher : Springer
Page : 214 pages
File Size : 40,7 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540682684

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Pseudo-Differential Operators by Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft Pdf

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

Author : Matthew J. Gursky,Ermanno Lanconelli,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 55,6 Mb
Release : 2009-06-26
Category : Mathematics
ISBN : 9783642016738

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Geometric Analysis and PDEs by Matthew J. Gursky,Ermanno Lanconelli,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang Pdf

This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.