Memoirs of the American Mathematical Society 2005; 99 pp; softcover Volume: 174 ISBN10: 0821836390 ISBN13: 9780821836392 List Price: US$63 Individual Members: US$37.80 Institutional Members: US$50.40 Order Code: MEMO/174/822
 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 OmoriYau 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. Readership Graduate students and research mathematicians interested in analysis and Riemannian geometry. Table of Contents  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
