Maximum Principles and Geometric Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximum Principles and Geometric Applications write by Luis J. Alías. This book was released on 2019-03-21. Maximum Principles and Geometric Applications available 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.
Maximum Principles and Geometric Applications
Maximum Principles and Geometric Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximum Principles and Geometric Applications write by Luis J. Alías. This book was released on 2016-02-13. Maximum Principles and Geometric Applications available 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.
Maximum Principles on Riemannian Manifolds and Applications
Maximum Principles on Riemannian Manifolds and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximum Principles on Riemannian Manifolds and Applications write by Stefano Pigola. This book was released on 2005. Maximum Principles on Riemannian Manifolds and Applications available 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.
Contemporary Research in Elliptic PDEs and Related Topics
Contemporary Research in Elliptic PDEs and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Contemporary Research in Elliptic PDEs and Related Topics write by Serena Dipierro. This book was released on 2019-07-12. Contemporary Research in Elliptic PDEs and Related Topics available 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.
Geometric Analysis of Quasilinear Inequalities on Complete Manifolds
Geometric Analysis of Quasilinear Inequalities on Complete Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Analysis of Quasilinear Inequalities on Complete Manifolds write by Bruno Bianchini. This book was released on 2021-01-18. Geometric Analysis of Quasilinear Inequalities on Complete Manifolds available 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.
