Vanishing And Finiteness Results In Geometric Analysis
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Vanishing And Finiteness Results In Geometric Analysis
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Author : Stefano Pigola
language : en
Publisher: Birkhäuser
Release Date : 2009-08-29
Vanishing And Finiteness Results In Geometric Analysis written by Stefano Pigola and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Mathematics categories.
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.
Vanishing And Finiteness Results In Geometric Analysis
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Author : Stefano Pigola
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-28
Vanishing And Finiteness Results In Geometric Analysis written by Stefano Pigola 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 2008-05-28 with Mathematics categories.
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.
Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds
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Author : Bruno Bianchini
language : en
Publisher: Springer Nature
Release Date : 2021-01-18
Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds written by Bruno Bianchini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.
This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Geometric Potential Analysis
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Author : Mario Milman
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-06-21
Geometric Potential Analysis written by Mario Milman and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-21 with Science categories.
This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.
Topics In Modern Differential Geometry
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Author : Stefan Haesen
language : en
Publisher: Springer
Release Date : 2016-12-21
Topics In Modern Differential Geometry written by Stefan Haesen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-21 with Mathematics categories.
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Recent Advances In The Geometry Of Submanifolds
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Author : Bogdan D. Suceavă
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-14
Recent Advances In The Geometry Of Submanifolds written by Bogdan D. Suceavă 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 2016-09-14 with Differential geometry -- Local differential geometry -- Local submanifolds categories.
This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, held from October 25–26, 2014, at San Francisco State University, San Francisco, CA, and the AMS Special Session on Recent Advances in the Geometry of Submanifolds: Dedicated to the Memory of Franki Dillen (1963–2013), held from March 14–15, 2015, at Michigan State University, East Lansing, Ml. The focus of the volume is on recent studies of submanifolds of Riemannian, semi-Riemannian, Kaehlerian and contact manifolds. Some of these use techniques in classical differential geometry, while others use methods from ordinary differential equations, geometric analysis, or geometric PDEs. By brainstorming on the fundamental problems and exploring a large variety of questions studied in submanifold geometry, the editors hope to provide mathematicians with a working tool, not just a collection of individual contributions. This volume is dedicated to the memory of Franki Dillen, whose work in submanifold theory attracted the attention of and inspired many geometers.
The Ricci Flow In Riemannian Geometry
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Author : Ben Andrews
language : en
Publisher: Springer
Release Date : 2010-11-09
The Ricci Flow In Riemannian Geometry written by Ben Andrews and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-09 with Mathematics categories.
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.
Lorentzian Geometry And Related Topics
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Author : María A. Cañadas-Pinedo
language : en
Publisher: Springer
Release Date : 2018-03-06
Lorentzian Geometry And Related Topics written by María A. Cañadas-Pinedo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Mathematics categories.
This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.
Global Riemannian Geometry Curvature And Topology
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Author : Ana Hurtado
language : en
Publisher: Springer Nature
Release Date : 2020-08-19
Global Riemannian Geometry Curvature And Topology written by Ana Hurtado and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-19 with Mathematics categories.
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.
Stable Homotopy Around The Arf Kervaire Invariant
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Author : Victor P. Snaith
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-28
Stable Homotopy Around The Arf Kervaire Invariant written by Victor P. Snaith 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 2009-03-28 with Mathematics categories.
Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .