Some remarks on the Pigola-Rigoli-Setti version of the Omori-Yau maximum principle

Authors

  • A. P. Barreto Universidade Federal de São Carlos Departamento de Matemática
  • F. Fontenele Universidade Federal Fluminense Departamento de Geometria

Keywords:

maximum principles, Omori-Yau maximum principle

Abstract

We prove that the hypotheses in the Pigola–Rigoli–Setti version of the Omori–Yau maximum principle are logically equivalent to the assumption that the manifold carries a \(C^2\)proper function whose gradient and Hessian (Laplacian) are bounded. In particular, this result extends the scope of the original Omori-Yau principle, formulated in terms of lower bounds for curvature. 10.1017/S0004972713000634

Published

2014-01-27

Issue

Section

Articles