The aim of the paper is to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity recently obtained by the authors. Applications are given to a number of geometrical problems in the setting of complete Riemannian manifolds, under assumptions either on the curvature or on the volume growth of geodesic balls
Pigola, S., Rigoli, M., Setti, A. (2005). Maximum Principles on Riemannian Manifolds and Applications. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 174(822), 1-99 [10.1090/memo/0822].
Maximum Principles on Riemannian Manifolds and Applications
PIGOLA S.;
2005
Abstract
The aim of the paper is to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity recently obtained by the authors. Applications are given to a number of geometrical problems in the setting of complete Riemannian manifolds, under assumptions either on the curvature or on the volume growth of geodesic balls
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