Yamabe Type Equations On Complete Noncompact Manifolds

Author : Paolo Mastrolia,Marco Rigoli,Alberto G Setti
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 42,9 Mb
Release : 2012-07-30
Category : Mathematics
ISBN : 9783034803762

Get Book

Yamabe-type Equations on Complete, Noncompact Manifolds by Paolo Mastrolia,Marco Rigoli,Alberto G Setti Pdf

The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists. After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds.

Author : Bruno Bianchini,Luciano Mari,Marco Rigoli
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 40,5 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9780821887998

Get Book

On Some Aspects of Oscillation Theory and Geometry by Bruno Bianchini,Luciano Mari,Marco Rigoli Pdf

The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

Author : Luis J. Alías,Paolo Mastrolia,Marco Rigoli
Publisher : Springer
Page : 570 pages
File Size : 42,9 Mb
Release : 2016-02-13
Category : Mathematics
ISBN : 9783319243375

Get Book

Maximum Principles and Geometric Applications by Luis J. Alías,Paolo Mastrolia,Marco Rigoli Pdf

This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter. In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on. Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.

Author : Giovanni Catino,Paolo Mastrolia
Publisher : Springer Nature
Page : 247 pages
File Size : 50,8 Mb
Release : 2020-10-23
Category : Mathematics
ISBN : 9783030571856

Get Book

A Perspective on Canonical Riemannian Metrics by Giovanni Catino,Paolo Mastrolia Pdf

This book focuses on a selection of special topics, with emphasis on past and present research of the authors on “canonical” Riemannian metrics on smooth manifolds. On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of “Curvature Conditions” and “Critical Metrics” of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

Author : Bruno Bianchini,Luciano Mari,Patrizia Pucci,Marco Rigoli
Publisher : Springer Nature
Page : 291 pages
File Size : 42,9 Mb
Release : 2021-01-18
Category : Mathematics
ISBN : 9783030627041

Get Book

Geometric Analysis of Quasilinear Inequalities on Complete Manifolds by Bruno Bianchini,Luciano Mari,Patrizia Pucci,Marco Rigoli Pdf

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.

Author : James B. Serrin,Enzo L. Mitidieri,Vicenţiu D. Rădulescu
Publisher : American Mathematical Soc.
Page : 323 pages
File Size : 54,7 Mb
Release : 2013-07-22
Category : Mathematics
ISBN : 9780821887363

Get Book

Recent Trends in Nonlinear Partial Differential Equations I by James B. Serrin,Enzo L. Mitidieri,Vicenţiu D. Rădulescu Pdf

This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t

Author : Stefano Pigola,Marco Rigoli,Alberto G Setti
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 50,8 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 : Angela Slavova
Publisher : Springer Nature
Page : 457 pages
File Size : 45,7 Mb
Release : 2023-03-17
Category : Mathematics
ISBN : 9783031214844

Get Book

New Trends in the Applications of Differential Equations in Sciences by Angela Slavova Pdf

This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis. In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations. The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.

Author : Giovanni Molica Bisci,Patrizia Pucci
Publisher : Walter de Gruyter GmbH & Co KG
Page : 290 pages
File Size : 42,7 Mb
Release : 2021-02-08
Category : Mathematics
ISBN : 9783110652017

Get Book

Nonlinear Problems with Lack of Compactness by Giovanni Molica Bisci,Patrizia Pucci Pdf

This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.

Author : Robert Everist Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 585 pages
File Size : 52,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821814949

Get Book

Differential Geometry: Partial Differential Equations on Manifolds by Robert Everist Greene,Shing-Tung Yau Pdf

The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem

Author : Abbas Bahri,Sergiu Klainerman,Michael Vogelius
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 45,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836354

Get Book

Noncompact Problems at the Intersection of Geometry, Analysis, and Topology by Abbas Bahri,Sergiu Klainerman,Michael Vogelius Pdf

This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. Mathematicians attending the conference had interests in noncompact variational problems, pseudo-holomorphic curves, singular and smooth solutions to problems admitting a conformal (or some group) invariance, Sobolev spaces on manifolds, and configuration spaces. One day of the proceedings was devoted to Einstein equations and related topics. Contributors to the volume include, among others, Sun-Yung A. Chang, Luis A. Caffarelli, Carlos E. Kenig, and Gang Tian. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.

Author : Anonim
Publisher : Unknown
Page : 504 pages
File Size : 44,6 Mb
Release : 2007
Category : Differential equations
ISBN : UOM:39015072600516

Get Book

Differential and Integral Equations by Anonim Pdf

Author : Shiing-shen Chern
Publisher : Springer
Page : 301 pages
File Size : 48,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391074

Get Book

Partial Differential Equations by Shiing-shen Chern Pdf

The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

Author : Jerry L. Kazdan
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 51,9 Mb
Release : 1985-12-31
Category : Mathematics
ISBN : 0821889028

Get Book

Prescribing the Curvature of a Riemannian Manifold by Jerry L. Kazdan Pdf

These notes were the basis for a series of ten lectures given in January 1984 at Polytechnic Institute of New York under the sponsorship of the Conference Board of the Mathematical Sciences and the National Science Foundation. The lectures were aimed at mathematicians who knew either some differential geometry or partial differential equations, although others could understand the lectures. Author's Summary:Given a Riemannian Manifold $(M,g)$ one can compute the sectional, Ricci, and scalar curvatures. In other special circumstances one also has mean curvatures, holomorphic curvatures, etc. The inverse problem is, given a candidate for some curvature, to determine if there is some metric $g$ with that as its curvature. One may also restrict ones attention to a special class of metrics, such as Kahler or conformal metrics, or those coming from an embedding. These problems lead one to (try to) solve nonlinear partial differential equations. However, there may be topological or analytic obstructions to solving these equations. A discussion of these problems thus requires a balanced understanding between various existence and non-existence results. The intent of this volume is to give an up-to-date survey of these questions, including enough background, so that the current research literature is accessible to mathematicians who are not necessarily experts in PDE or differential geometry. The intended audience is mathematicians and graduate students who know either PDE or differential geometry at roughly the level of an intermediate graduate course.

Author : Anonim
Publisher : Unknown
Page : 1226 pages
File Size : 54,9 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015082440861

Get Book

Mathematical Reviews by Anonim Pdf