On some aspects of oscillation theory and geometry
Author(s)
Bibliographic Information
On some aspects of oscillation theory and geometry
（Memoirs of the American Mathematical Society, no. 1056）
American Mathematical Society, 2013
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"Volume 225, number 1056 (first of 4 numbers), September 2013"
Includes bibliographical references (p. 187-195)
Description and Table of Contents
Description
The aim of this paper is to analyse some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.
Table of Contents
Introduction The geometric setting Some geometric examples related to oscillation theory On the solutions of the ODE $(vz')' Avz=0$ Below the critical curve Exceeding the critical curve Much above the critical curve Bibliography
by "Nielsen BookData"