Maximum Principles and Geometric Applications

• Main Authors: Alías, Luis J. (Author), Mastrolia, Paolo (Author), Rigoli, Marco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Edition: 1st ed. 2016.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Geometry.; Global Analysis and Analysis on Manifolds.; Partial Differential Equations.

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 partic...

Table of 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.