The aim of this 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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ISBN-13
978-0-8218-3639-2 (9780821836392)
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Schweitzer Klassifikation
Preliminaries and some geometric motivations Further typical applications of Yau's technique Stochastic completeness and the weak maximum principle The weak maximum principle for the $\varphi$-Laplacian $\varphi$-parabolicity and some further remarks Curvature and the maximum principle for the $\varphi$-Laplacian Bibliography.
