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Springer Monographs in Mathematics

Maximum Principles and Geometric Applications

Authors: Alías, Luis J., Mastrolia, Paolo, Rigoli, Marco

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  • 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
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-24337-5
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Hardcover $149.99
price for USA in USD
  • ISBN 978-3-319-24335-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-3-319-79605-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

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)


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-24337-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-319-24335-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-3-319-79605-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Maximum Principles and Geometric Applications
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-24337-5
DOI
10.1007/978-3-319-24337-5
Hardcover ISBN
978-3-319-24335-1
Softcover ISBN
978-3-319-79605-5
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XXVII, 570
Topics