Journal of Geometric Analysis

, Volume 22, Issue 3, pp 763–779

Myers-Type Theorems and Some Related Oscillation Results

  • Paolo Mastrolia
  • Michele Rimoldi
  • Giona Veronelli
Article

DOI: 10.1007/s12220-011-9213-0

Cite this article as:
Mastrolia, P., Rimoldi, M. & Veronelli, G. J Geom Anal (2012) 22: 763. doi:10.1007/s12220-011-9213-0

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 Schrödinger operators on complete manifolds.

Keywords

Myers-type theoremsOscillationPositioning of zeros

Mathematics Subject Classification (2000)

53C2034C10

Copyright information

© Mathematica Josephina, Inc. 2011

Authors and Affiliations

  • Paolo Mastrolia
    • 1
  • Michele Rimoldi
    • 1
  • Giona Veronelli
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly