Download or read book Comparison Theorems in Riemannian Geometry written by Jeff Cheeger and published by Newnes. This book was released on 2009-01-15 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comparison Theorems in Riemannian Geometry

Download or read book Comparison Theorems in Riemannian Geometry written by Jeff Cheeger and published by . This book was released on 1975 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Comparison Theorems in Riemennian Geometry written by Jeff Cheeger and published by . This book was released on 1975 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Comparison Geometry written by Karsten Grove and published by Cambridge University Press. This book was released on 1997-05-13 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an up to date work on a branch of Riemannian geometry called Comparison Geometry.

Download or read book Riemannian Geometry written by Peter Petersen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Riemannian Geometry written by Takashi Sakai and published by American Mathematical Soc.. This book was released on 1996-01-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Riemannian Geometry written by Gérard Besson and published by American Mathematical Soc.. This book was released on 1996-01-01 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Riemann Finsler Geometry written by D. Bao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Comparison Finsler Geometry written by Shin-ichi Ohta and published by Springer Nature. This book was released on 2021-10-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Global Riemannian Geometry Curvature and Topology written by Steen Markvorsen and published by Birkhäuser. This book was released on 2012-12-06 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Introduction to Riemannian Manifolds written by John M. Lee and published by Springer. This book was released on 2019-01-02 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Riemannian Geometry and Geometric Analysis written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Riemannian Geometry written by Isaac Chavel and published by Cambridge University Press. This book was released on 1995-01-27 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.

Download or read book Riemannian Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Ricci Flow in Riemannian Geometry written by Ben Andrews and published by Springer Science & Business Media. This book was released on 2011 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Global Riemannian Geometry written by Thomas Willmore and published by . This book was released on 1984 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry of Manifolds written by Richard L. Bishop and published by American Mathematical Soc.. This book was released on 2001 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface of the First Edition: ``Our purpose in writing this book is to put material which we found stimulating and interesting as graduate students into form. It is intended for individual study and for use as a text for graduate level courses such as the one from which this material stems, given by Professor W. Ambrose at MIT in 1958-1959. Previously the material had been organized in roughly the same form by him and Professor I. M. Singer, and they in turn drew upon thework of Ehresmann, Chern, and E. Cartan. Our contributions have been primarily to fill out the material with details, asides and problems, and to alter notation slightly. ``We believe that this subject matter, besides being an interesting area for specialization, lends itself especially to a synthesisof several branches of mathematics, and thus should be studied by a wide spectrum of graduate students so as to break away from narrow specialization and see how their own fields are related and applied in other fields. We feel that at least part of this subject should be of interest not only to those working in geometry, but also to those in analysis, topology, algebra, and even probability and astronomy. In order that this book be meaningful, the reader's background should include realvariable theory, linear algebra, and point set topology.'' This volume is a reprint with few corrections of the original work published in 1964. Starting with the notion of differential manifolds, the first six chapters lay a foundation for the study of Riemannian manifolds through specializing the theoryof connections on principle bundles and affine connections. The geometry of Riemannian manifolds is emphasized, as opposed to global analysis, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory. Isometric immersions are treated elegantly and from a global viewpoint. In the final chapter are the more complicated estimates on which much of the research in Riemannian geometry is based: the Morse index theorem,Synge's theorems on closed geodesics, Rauch's comparison theorem, and the original proof of the Bishop volume-comparison theorem (with Myer's Theorem as a corollary). The first edition of this book was the origin of a modern treatment of global Riemannian geometry, using the carefully conceived notationthat has withstood the test of time. The primary source material for the book were the papers and course notes of brilliant geometers, including E. Cartan, C. Ehresmann, I. M. Singer, and W. Ambrose. It is tightly organized, uniformly very precise, and amazingly comprehensive for its length.