English

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

Differential Geometry 2014-09-26 v4

Abstract

We generalize A. Borb\'ely'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 LL 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.

Keywords

Cite

@article{arxiv.1309.7725,
  title  = {A remark on the Omori-Yau maximum principle for semi-elliptic operators},
  author = {Kyusik Hong},
  journal= {arXiv preprint arXiv:1309.7725},
  year   = {2014}
}

Comments

12 pages; This paper has been withdrawn by the author.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