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Author : Gábor Tóth (Ph. D.)
Publisher : Unknown
Page : 176 pages
File Size : 45,9 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018970650
Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 240 pages
File Size : 55,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882502
The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Author : Gabor Toth
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461300618
"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. In this accessible book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including a valuable selection of exercises.
Author : Anonim
Publisher : Elsevier
Page : 343 pages
File Size : 42,8 Mb
Release : 1996-09-27
Category : Mathematics
ISBN : 9780080526959
This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike. Presents several different points of view on key topics in representation theory, from internationally known experts in the field
Author : Hajime Urakawa
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 50,6 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9780821894132
This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science. Containing many examples, open problems, and exercises with complete solutions, the book would be suitable as a text for graduate courses in differential geometry, partial differential equations, and variational methods. The first part of the book is devoted to explaining the notion of (infinite-dimensional) manifolds and contains many examples. An introduction to Morse theory of Banach manifolds is provided, along with a proof of the existence of minimizing functions under the Palais-Smale condition. The second part, which may be read independently of the first, presents the theory of harmonic maps, with a careful calculation of the first and second variations of the energy. Several applications of the second variation and classification theories of harmonic maps are given.
Author : Paul Baird,John C. Wood
Publisher : Oxford University Press
Page : 540 pages
File Size : 40,7 Mb
Release : 2003
Category : Mathematics
ISBN : 0198503628
This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 238 pages
File Size : 51,5 Mb
Release : 1993
Category : Mathematics
ISBN : 069110249X
The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Author : Gestur Olafsson,Joachim Hilgert
Publisher : Academic Press
Page : 303 pages
File Size : 49,6 Mb
Release : 1996-09-11
Category : Mathematics
ISBN : 9780080528724
This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces. Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spaces Deals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fields Presents basic geometric properties of semi-simple symmetric spaces Includes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
Author : Jurgen Berndt,Sergio Console,Carlos Enrique Olmos
Publisher : CRC Press
Page : 494 pages
File Size : 41,6 Mb
Release : 2016-02-22
Category : Mathematics
ISBN : 9781482245165
Submanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor.New to the Second EditionNew chapter on normal holonom
Author : Valentino Cristante,William Messing
Publisher : Academic Press
Page : 306 pages
File Size : 42,7 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781483217628
Barsotti Symposium in Algebraic Geometry contains papers corresponding to the lectures given at the 1991 memorial meeting held in Abano Terme in honor of Iacopo Barsotti. This text reflects Barsotti’s significant contributions in the field. This book is composed of 10 chapters and begins with a review of the centers of three-dimensional skylanin algebras. The succeeding chapters deal with the theoretical aspects of the Abelian varieties, Witt realization of p-Adic Barsotti-Tate Groups, and hypergeometric series and functions. These topics are followed by discussions of logarithmic spaces and the estimates for and inequalities among A-numbers. The closing chapter describes the moduli of Abelian varieties in positive characteristic. This book will be of value to mathematicians.
Author : Roger Howe,Markus Hunziker,Jeb F. Willenbring
Publisher : Springer
Page : 562 pages
File Size : 52,5 Mb
Release : 2015-01-04
Category : Mathematics
ISBN : 9781493915903
Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.
Author : James W. Cogdell,Iiya Piatetski-Shapiro
Publisher : Academic Press
Page : 190 pages
File Size : 40,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781483266176
The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is analyzed, along with the adellic theory of Poincaré series and Kloosterman sums over a global function field. This volume is divided into two parts and begins with a discussion on Poincaré series and Kloosterman sums for Fuchsian groups of the first kind. A conceptual proof of Kuznetsov's formula and its generalization are presented in terms of the spectral analysis of Poincaré series in the framework of representation theory. An analysis of the spectral expansion of the Kloosterman-Selberg zeta function is also included. The second part develops the adellic theory of Poincaré series and Kloosterman sums over a global function field. The main result here is to show that in this context the analogue of the Linnik conjecture can be derived from the Ramanujan conjecture over function fields. Whittaker models, Kirillov models, and Bessel functions are also considered, along with the Kloosterman-spectral formula, convergence, and continuation. This book will be a valuable resource for students of mathematics.
Author : D Gieseker
Publisher : Academic Press
Page : 246 pages
File Size : 52,8 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780323159289
The Geometry of Algebraic Fermi Curves deals with the geometry of algebraic Fermi curves, with emphasis on the inverse spectral problem. Topics covered include the periodic Schrödinger operator and electrons in a crystal; one-dimensional algebraic Bloch varieties; separable Bloch varieties; and monodromy for separable and generic Bloch varieties. Compactification, the potential zero, and density of states are also discussed. This book consists of 13 chapters and begins by recalling the static lattice approximation for electronic motion at low temperature in a pure, finite sample of a d-dimensional crystal. The position of the Fermi energy and the geometry of the Fermi hypersurface in relation to the metallic properties of the crystal are described. The following chapters focus on the Bloch variety associated with a discrete two-dimensional periodic Schrödinger operator; algebraic Bloch varieties in one dimension; compactification of the Bloch variety; and the potential zero. The geometry of the Bloch variety of a separable potential is also considered, along with the topology of the family of Fermi curves. The final chapter demonstrates how the Bloch variety is determined by the density of states. This monograph will be a useful resource for students and teachers of mathematics.
Author : Daniel B. Shapiro
Publisher : Walter de Gruyter
Page : 433 pages
File Size : 40,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110824834
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Author : Malcolm Black
Publisher : Routledge
Page : 63 pages
File Size : 55,7 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351441612
Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.
