Spectral estimates for Dirichlet Laplacian on spiral-shaped regions

TL;DR

This paper derives spectral estimates of Lieb-Thirring type for the eigenvalues of Dirichlet Laplacians on spiral-shaped regions that are strictly shrinking, providing new bounds for these eigenvalues.

Contribution

It introduces novel spectral estimates specifically for Dirichlet Laplacians on shrinking spiral-shaped domains, extending existing spectral theory.

Findings

Spectral bounds for eigenvalues on spiral domains

Extension of Lieb-Thirring inequalities to non-standard geometries

Eigenvalue estimates depend on the geometry of the spiral regions

Abstract

We derive spectral estimates of the Lieb-Thirring type for eigenvalues of Dirichlet Laplacians on strictly shrinking spiral-shaped domains.