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Maximum principles and geometric applications / by Luis J. Alías, Paolo Mastrolia, Marco Rigoli.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- Alías, Luis J., Author.
- Mastrolia, Paolo, Author.
- Rigoli, Marco, Author.
- Series:
- Springer Monographs in Mathematics, 1439-7382
- Language:
- English
- Subjects (All):
- Global analysis (Mathematics).
- Manifolds (Mathematics).
- Differential equations, Partial.
- Geometry.
- Global Analysis and Analysis on Manifolds.
- Partial Differential Equations.
- Local Subjects:
- Global Analysis and Analysis on Manifolds.
- Partial Differential Equations.
- Geometry.
- Physical Description:
- 1 online resource (594 p.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- Language Note:
- English
- 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.
- Contents:
- 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.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references and index.
- ISBN:
- 3-319-24337-3
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