Overview
- Provides a self-contained approach to the study of geometric and analytic aspects of maximum principles, making it a perfect companion to other books on the subject
- Presents the essential analytic tools and the geometric foundations needed to understand maximum principles and their geometric applications
- Includes a wide range of applications of maximum principles to different geometric problems, including some topics that are rare in current literature such as Ricci solitons
- Relevant to other areas of mathematics, namely, partial differential equations on manifolds, calculus of variations, and probabilistic potential theory
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 GeometricApplications 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.
Reviews
“This is a very well-written book on an active area of research appealing to geometers and analysts alike, whether they are specialists in the field, or they simply desire to learn the techniques. Moreover, the applications included in this volume encompass a variety of directions with an accent on the geometry of hypersurfaces, while the high number of references dating from 2000 or later are a testimonial of the state of the art developments presented in this volume.” (Alina Stancu, zbMATH 1346.58001, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Maximum Principles and Geometric Applications
Authors: Luis J. Alías, Paolo Mastrolia, Marco Rigoli
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-24337-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-24335-1Published: 22 February 2016
Softcover ISBN: 978-3-319-79605-5Published: 21 March 2019
eBook ISBN: 978-3-319-24337-5Published: 13 February 2016
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XXVII, 570
Topics: Global Analysis and Analysis on Manifolds, Partial Differential Equations, Geometry