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Author : Jeff Cheeger,David G. Ebin
Publisher : Newnes
Page : 183 pages
File Size : 47,6 Mb
Release : 2009-01-15
Category : Computers
ISBN : 9780444107640
Comparison Theorems in Riemannian Geometry
Author : Jeff Cheeger,D. G. Ebin
Publisher : Unknown
Page : 174 pages
File Size : 49,8 Mb
Release : 1975
Category : Geometry, Riemannian
ISBN : 0080960073
Author : Jeff Cheeger,David Gregory Ebin
Publisher : Unknown
Page : 174 pages
File Size : 47,6 Mb
Release : 1975
Category : Electronic
ISBN : 072042450X
Author : Jost-Hinrich Eschenburg
Publisher : Unknown
Page : 77 pages
File Size : 44,7 Mb
Release : 1994
Category : Geometry, Riemannian
ISBN : OCLC:79325007
Author : Karsten Grove,Peter Petersen
Publisher : Cambridge University Press
Page : 280 pages
File Size : 44,5 Mb
Release : 1997-05-13
Category : Mathematics
ISBN : 0521592224
This is an up to date work on a branch of Riemannian geometry called Comparison Geometry.
Author : Peter Petersen
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 41,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475764345
Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialise in Riemannian geometry. Instead of variational techniques, the author uses a unique approach, emphasising distance functions and special co-ordinate systems. He also uses standard calculus with some techniques from differential equations to provide a more elementary route. Many chapters contain material typically found in specialised texts, never before published in a single source. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research - including sections on convergence and compactness of families of manifolds. Thus, this book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject.
Author : Steen Markvorsen,Maung Min-Oo
Publisher : Birkhäuser
Page : 100 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880558
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 : Gérard Besson,Miroslav Lovric,Maung Min-Oo,McKenzie Yuen-kong Wang
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 43,8 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0821871870
This book is a compendium of survey lectures presented at a conference on Riemannian Geometry sponsored by The Fields Institute for Research in Mathematical Sciences (Waterloo, Canada) in August 1993. Attended by over 80 participants, the aim of the conference was to promote research activity in Riemannian geometry. A select group of internationally established researchers in the field were invited to discuss and present current developments in a selection of contemporary topics in Riemannian geometry. This volume contains four of the five survey lectures presented at the conference.
Author : Takashi Sakai
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 51,6 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0821889567
This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.
Author : John M. Lee
Publisher : Springer
Page : 437 pages
File Size : 43,6 Mb
Release : 2019-01-02
Category : Mathematics
ISBN : 9783319917559
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Author : D. Bao,S.-S. Chern,Z. Shen
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212683
This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.
Author : Ben Andrews,Christopher Hopper
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 42,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9783642162855
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 : Shin-ichi Ohta
Publisher : Springer Nature
Page : 324 pages
File Size : 46,9 Mb
Release : 2021-10-09
Category : Mathematics
ISBN : 9783030806507
This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.
Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 51,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662223857
FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."-MATHEMATICAL REVIEWS
Author : Victor Andreevich Toponogov
Publisher : Unknown
Page : 224 pages
File Size : 49,9 Mb
Release : 2011-03-21
Category : Electronic
ISBN : 0817670947