Riemannian Geometry And Geometric Analysis

Author : Jürgen Jost
Publisher : Springer
Page : 697 pages
File Size : 40,5 Mb
Release : 2017-10-13
Category : Mathematics
ISBN : 9783319618609

Get Book

Riemannian Geometry and Geometric Analysis by Jürgen Jost Pdf

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

Author : Jurgen Jost
Publisher : Unknown
Page : 422 pages
File Size : 41,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662031191

Get Book

Riemannian Geometry and Geometric Analysis by Jurgen Jost Pdf

Author : Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer
Publisher : Springer Nature
Page : 121 pages
File Size : 51,8 Mb
Release : 2020-08-19
Category : Mathematics
ISBN : 9783030552930

Get Book

Global Riemannian Geometry: Curvature and Topology by Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer Pdf

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.

Author : Xavier Pennec,Stefan Sommer,Tom Fletcher
Publisher : Academic Press
Page : 636 pages
File Size : 51,5 Mb
Release : 2019-09-02
Category : Computers
ISBN : 9780128147269

Get Book

Riemannian Geometric Statistics in Medical Image Analysis by Xavier Pennec,Stefan Sommer,Tom Fletcher Pdf

Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology Content includes: The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs Applications of statistics on manifolds and shape spaces in medical image computing Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. A complete reference covering both the foundations and state-of-the-art methods Edited and authored by leading researchers in the field Contains theory, examples, applications, and algorithms Gives an overview of current research challenges and future applications

Author : Stefano Pigola,Marco Rigoli,Alberto G Setti
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 55,6 Mb
Release : 2008-05-28
Category : Mathematics
ISBN : 9783764386429

Get Book

Vanishing and Finiteness Results in Geometric Analysis by Stefano Pigola,Marco Rigoli,Alberto G Setti Pdf

This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.

Author : Thierry Aubin
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 49,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662130063

Get Book

Some Nonlinear Problems in Riemannian Geometry by Thierry Aubin Pdf

This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.

Author : John Bland,Kang-Tae Kim,Steven George Krantz
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 47,7 Mb
Release : 2003
Category : Differential geometry
ISBN : 9780821832738

Get Book

Explorations in Complex and Riemannian Geometry by John Bland,Kang-Tae Kim,Steven George Krantz Pdf

This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.

Author : Ovidiu Calin,Der-Chen Chang
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 46,5 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780817644215

Get Book

Geometric Mechanics on Riemannian Manifolds by Ovidiu Calin,Der-Chen Chang Pdf

* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Author : Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 53,5 Mb
Release : 2016-05-18
Category : Geometric analysis
ISBN : 9781470423131

Get Book

Geometric Analysis by Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum Pdf

This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Author : Bernhard Riemann
Publisher : Birkhäuser
Page : 172 pages
File Size : 44,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9783319260426

Get Book

On the Hypotheses Which Lie at the Bases of Geometry by Bernhard Riemann Pdf

This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.

Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 45,9 Mb
Release : 2008-06-24
Category : Mathematics
ISBN : 9783540773412

Get Book

Riemannian Geometry and Geometric Analysis by Jürgen Jost Pdf

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. This new edition introduces and explains the ideas of the parabolic methods that have recently found such spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.

Author : Leonor Godinho,José Natário
Publisher : Springer
Page : 476 pages
File Size : 55,9 Mb
Release : 2014-07-26
Category : Mathematics
ISBN : 9783319086668

Get Book

An Introduction to Riemannian Geometry by Leonor Godinho,José Natário Pdf

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Author : Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 53,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821838396

Get Book

An Introduction to the Analysis of Paths on a Riemannian Manifold by Daniel W. Stroock Pdf

Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Peter Li
Publisher : Cambridge University Press
Page : 417 pages
File Size : 41,5 Mb
Release : 2012-05-03
Category : Mathematics
ISBN : 9781107020641

Get Book

Geometric Analysis by Peter Li Pdf

This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis.

Author : Iva Stavrov
Publisher : American Mathematical Soc.
Page : 243 pages
File Size : 53,9 Mb
Release : 2020-11-12
Category : Education
ISBN : 9781470456283

Get Book

Curvature of Space and Time, with an Introduction to Geometric Analysis by Iva Stavrov Pdf

This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.