Inequalities for eigenvalues of Laplacian and biharmonic operators on submanifolds

TL;DR

This paper derives new inequalities for the eigenvalues of Laplacian and biharmonic operators on submanifolds, using Sobolev inequalities, advancing understanding of spectral properties in geometric analysis.

Contribution

It introduces novel eigenvalue inequalities for Laplacian and biharmonic operators on submanifolds, utilizing Sobolev inequalities, which were not previously established.

Findings

New eigenvalue inequalities for Laplacian operators

New eigenvalue inequalities for biharmonic operators

Use of Sobolev inequalities to derive these bounds

Abstract

In this paper we study eigenvalues of Laplacian and biharmonic operators on compact domains in complete manifolds. We establish several new inequalities for eigenvalues of Laplacian and biharmonic operators respectively by using Sobolev type inequalities.