Myers' type theorems and some related oscillation results

Abstract

In this paper we study the behavior of solutions of a second order differential equation. The existence of a zero and its localization allow us to get some compactness results. In particular we obtain a Myers' type theorem even in the presence of an amount of negative curvature. The technique we use also applies to the study of spectral properties of Schroedinger operators on complete manifolds.

16 pages

Cited by in corpus (4)

• A remark on Einstein warped products
• Myers' type theorem with the Bakry-Émery Ricci tensor
• Extensions of Bonnet-Myers' type theorems with the Bakry-Emery Ricci curvature
• Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem