preprint

Inserted: 4 dec 2020

Year: 2017

Abstract:

We provide several inequalities between eigenvalues of some classical eigenvalue problems on domains with $C^2$ boundary in complete Riemannian manifolds. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kutller and Sigillito from subsets of $\mathbb{R}^2$ to the manifold setting.