Positive and negative growth rates of measures and pointwise bounds of solutions of eigenvalue equations

TL;DR

This paper investigates the growth behavior of measures and provides pointwise bounds for solutions to eigenvalue equations involving the Laplace-Beltrami operator on noncompact Riemannian manifolds, enhancing understanding of their spectral properties.

Contribution

It introduces new pointwise bounds for solutions of eigenvalue equations on noncompact Riemannian manifolds, focusing on measure growth rates.

Findings

Derived bounds for solutions of eigenvalue equations

Analyzed growth rates of measures

Enhanced understanding of spectral properties

Abstract

This paper, focusing on the growth rate of the measure, gives pointwise bounds of solutions of eigenvalue equations of the Laplace-Beltrami operator on noncompact Riemannian manifolds.