Surveys In Differential Geometry Vol 7
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Surveys In Differential Geometry Vol 7
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Author : Yau
language : en
Publisher:
Release Date : 2010-04-30
Surveys In Differential Geometry Vol 7 written by Yau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-30 with Mathematics categories.
Collected Works
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Author : Michael Francis Atiyah
language : en
Publisher: Oxford University Press, USA
Release Date : 2014
Collected Works written by Michael Francis Atiyah and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.
Global Differential Geometry
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Author : Christian Bär
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-18
Global Differential Geometry written by Christian Bär 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 2011-12-18 with Mathematics categories.
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Surveys In Differential Geometry
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Author : Shing-Tung Yau
language : en
Publisher:
Release Date : 2003
Surveys In Differential Geometry written by Shing-Tung Yau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Algebraic topology categories.
Collected Papers Of John Milnor
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Author : John Willard Milnor
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Collected Papers Of John Milnor written by John Willard Milnor 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 1994 with Algebra categories.
The Ricci Flow Techniques And Applications
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Author : Bennett Chow
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-04-21
The Ricci Flow Techniques And Applications written by Bennett Chow 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 2010-04-21 with Mathematics categories.
The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.
The Ricci Flow An Introduction
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Author : Bennett Chow
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
The Ricci Flow An Introduction written by Bennett Chow 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 2004 with Mathematics categories.
The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to 'flow' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of manifolds.This book is an introduction to that program and to its connection to Thurston's geometrization conjecture. The authors also provide a 'Guide for the hurried reader', to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called 'fast track'. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds. "The Ricci Flow" was nominated for the 2005 Robert W. Hamilton Book Award, which is the highest honor of literary achievement given to published authors at the University of Texas at Austin.
Recent Advances In Alexandrov Geometry
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Author : Gerardo Arizmendi Echegaray
language : en
Publisher: Springer Nature
Release Date : 2022-10-27
Recent Advances In Alexandrov Geometry written by Gerardo Arizmendi Echegaray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with Mathematics categories.
This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen’s part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs. The text from Fernando Galaz-García’s minicourse was completed in collaboration with Jesús Nuñez-Zimbrón. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces. Jesús Nuñez-Zimbrón’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.
Variational Problems In Riemannian Geometry
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Author : Paul Baird
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Variational Problems In Riemannian Geometry written by Paul Baird and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.
Ricci Flow And The Poincare Conjecture
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Author : John W. Morgan
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Ricci Flow And The Poincare Conjecture written by John W. Morgan 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 2007 with Mathematics categories.
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).