The Weyl-type asymptotic formula for biharmonic Stekloff eigenvalues with Neumann boundary condition in Riemannian manifolds

TL;DR

This paper derives a Weyl-type asymptotic formula for the distribution of biharmonic Stekloff eigenvalues with Neumann boundary conditions in bounded domains within Riemannian manifolds, advancing spectral geometry understanding.

Contribution

It introduces a novel method to establish the asymptotic behavior of biharmonic Stekloff eigenvalues in Riemannian manifolds, filling a gap in spectral analysis of higher-order operators.

Findings

Established Weyl-type asymptotic formula for eigenvalue counting function

Applied new method to biharmonic Stekloff eigenvalues with Neumann boundary conditions

Extended spectral asymptotics to Riemannian manifold settings

Abstract

In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an $n$-dimensional Riemannian manifold.