A remark on the Omori-Yau maximum principle for semi-elliptic operators

Abstract

We generalize A. Borbély's condition for the conclusion of the Omori-Yau maximum principle for the Laplace operator on a complete Riemannian manifold to a second-order linear semi-elliptic operator $L$ with bounded coefficients and no zeroth order term. Also, we consider a new sufficient condition for the existence of a tamed exhaustion function. As a corollary, we show that the existence of a tamed exhaustion function is more general than the hypotheses in the version of the Omori-Yau maximum principle that was given by A. Ratto, M. Rigoli and A.G. Setti.

arXiv comment12 pages; This paper has been withdrawn by the author. A substantially altered paper will be submitted incorporating major corrections, additions and improvements

References in corpus (1)

• Maximum principle for semi-elliptic trace operators and geometric applications