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Maximum principles and geometric applications [electronic resource] / Luis J. Alías, Paolo Mastrolia, Marco Rigoli.

Alías, Luis J., author.; Mastrolia, Paolo, author.; Rigoli, Marco, author.
2016
QA377
Available Online
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Title
Maximum principles and geometric applications [electronic resource] / Luis J. Alías, Paolo Mastrolia, Marco Rigoli.
Author
Alías, Luis J., author.
ISBN
9783319243375 (electronic book)
3319243373 (electronic book)
9783319243351
DOI
https://doi.org/10.1007/978-3-319-24337-5
Published
Cham : Springer, 2016.
Language
English
Description
1 online resource (xxvii, 570 pages).
Item Number
10.1007/978-3-319-24337-5 doi
Call Number
QA377
Dewey Decimal Classification
515/.353
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 18, 2016).
Added Author
Mastrolia, Paolo, author.
Rigoli, Marco, author.
Series
Springer monographs in mathematics.
Available in Other Form
Print version: 9783319243351
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Online Access
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All Resources
A crash course in Riemannian geometry
The Omori-Yau maximum principle
New forms of the maximum principle
Sufficient conditions for the validity of the weak maximum principle
Miscellany results for submanifolds
Applications to hypersurfaces
Hypersurfaces in warped products
Applications to Ricci Solitons
Spacelike hypersurfaces in Lorentzian spacetimes.

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