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| Author | : Luis J. Alías |
| Publisher | : Springer |
| Total Pages | : 594 |
| Release | : 2016-02-13 |
| Genre | : Mathematics |
| ISBN | : 3319243373 |
Download Maximum Principles and Geometric Applications Book in PDF, ePub and Kindle
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 | : Stefano Pigola |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 118 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821836390 |
Download Maximum Principles on Riemannian Manifolds and Applications Book in PDF, ePub and Kindle
Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
| Author | : Serena Dipierro |
| Publisher | : Springer |
| Total Pages | : 502 |
| Release | : 2019-07-12 |
| Genre | : Mathematics |
| ISBN | : 303018921X |
Download Contemporary Research in Elliptic PDEs and Related Topics Book in PDF, ePub and Kindle
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
| Author | : Bruno Bianchini |
| Publisher | : Springer Nature |
| Total Pages | : 291 |
| Release | : 2021-01-18 |
| Genre | : Mathematics |
| ISBN | : 3030627047 |
Download Geometric Analysis of Quasilinear Inequalities on Complete Manifolds Book in PDF, ePub and Kindle
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 | : Qun Chen |
| Publisher | : |
| Total Pages | : |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
Download Omori-Yau Maximum Principles, V-harmonic Maps and Their Geometric Applications Book in PDF, ePub and Kindle
| Author | : Sperb |
| Publisher | : Academic Press |
| Total Pages | : 235 |
| Release | : 1981-07-28 |
| Genre | : Computers |
| ISBN | : 0080956645 |
Download Maximum Principles and Their Applications Book in PDF, ePub and Kindle
Maximum Principles and Their Applications
| Author | : Michel Boileau |
| Publisher | : Springer |
| Total Pages | : 149 |
| Release | : 2016-09-09 |
| Genre | : Mathematics |
| ISBN | : 3319423517 |
Download Ricci Flow and Geometric Applications Book in PDF, ePub and Kindle
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.
| Author | : Stefano Biagi |
| Publisher | : World Scientific |
| Total Pages | : 450 |
| Release | : 2018-12-05 |
| Genre | : Mathematics |
| ISBN | : 9813276630 |
Download An Introduction To The Geometrical Analysis Of Vector Fields: With Applications To Maximum Principles And Lie Groups Book in PDF, ePub and Kindle
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
| Author | : Vladimir Rovenski |
| Publisher | : Springer Nature |
| Total Pages | : 323 |
| Release | : |
| Genre | : |
| ISBN | : 3031505867 |
Download Differential Geometric Structures and Applications Book in PDF, ePub and Kindle
| Author | : Antonio Alarcón |
| Publisher | : Springer Nature |
| Total Pages | : 398 |
| Release | : 2023-11-25 |
| Genre | : Mathematics |
| ISBN | : 3031399161 |
Download New Trends in Geometric Analysis Book in PDF, ePub and Kindle
The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes. On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of them authored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG. Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.
