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

Abstract

We prove that the hypotheses in the version of the Omori-Yau maximum principle that was given by Pigola-Rigoli-Setti 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.

References in corpus (1)

• The mean curvature of cylindrically bounded submanifolds

Cited by in corpus (1)

• Bi-Halfspace and Convex Hull Theorems for Translating Solitons