Geometric Analysis
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Geometric Analysis
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Author : Peter Li
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-03
Geometric Analysis written by Peter Li and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-03 with Mathematics categories.
This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis.
Geometric Analysis
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Author : Ailana Fraser
language : en
Publisher: Springer Nature
Release Date : 2020-08-20
Geometric Analysis written by Ailana Fraser and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-20 with Mathematics categories.
This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces. An output of the CIME Summer School "Geometric Analysis" held in Cetraro in 2018, it offers a collection of lecture notes prepared by Ailana Fraser (UBC), André Neves (Chicago), Peter M. Topping (Warwick), and Paul C. Yang (Princeton). These notes will be a valuable asset for researchers and advanced graduate students in geometric analysis.
Geometric Analysis And Pdes
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Author : Matthew J. Gursky
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-26
Geometric Analysis And Pdes written by Matthew J. Gursky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-26 with Mathematics categories.
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.
Groups And Geometric Analysis
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-17
Groups And Geometric Analysis written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-17 with Mathematics categories.
Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.
Riemannian Geometry And Geometric Analysis
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Author : Jürgen Jost
language : en
Publisher: Springer
Release Date : 2017-10-13
Riemannian Geometry And Geometric Analysis written by Jürgen Jost and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-13 with Mathematics categories.
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews “For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik
Geometrical Vectors
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Author : Gabriel Weinreich
language : en
Publisher: University of Chicago Press
Release Date : 1998-07-06
Geometrical Vectors written by Gabriel Weinreich and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-06 with Mathematics categories.
Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.
Geometric Analysis Of The Bergman Kernel And Metric
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-20
Geometric Analysis Of The Bergman Kernel And Metric written by Steven G. Krantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-20 with Mathematics categories.
This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.
Convex Geometric Analysis
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Author : Keith M. Ball
language : en
Publisher: Cambridge University Press
Release Date : 1999-01-28
Convex Geometric Analysis written by Keith M. Ball and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-28 with Mathematics categories.
Convex geometry is at once simple and amazingly rich. While the classical results go back many decades, during that previous to this book's publication in 1999, the integral geometry of convex bodies had undergone a dramatic revitalization, brought about by the introduction of methods, results and, most importantly, new viewpoints, from probability theory, harmonic analysis and the geometry of finite-dimensional normed spaces. This book is a collection of research and expository articles on convex geometry and probability, suitable for researchers and graduate students in several branches of mathematics coming under the broad heading of 'Geometric Functional Analysis'. It continues the Israel GAFA Seminar series, which is widely recognized as the most useful research source in the area. The collection reflects the work done at the program in Convex Geometry and Geometric Analysis that took place at MSRI in 1996.
Geometric Analysis And Integral Geometry
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Author : Eric Todd Quinto
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Geometric Analysis And Integral Geometry written by Eric Todd Quinto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Olafsson and Robert Stanton.
Riemannian Geometry And Geometric Analysis
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-28
Riemannian Geometry And Geometric Analysis written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-28 with Mathematics categories.
This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews "...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH