The Dirichlet isospectral problem for trapezoids

TL;DR

This paper proves that non-obtuse trapezoids can be uniquely identified by their Dirichlet Laplace spectrum, extending previous work that only considered the Neumann spectrum, thus advancing spectral geometry understanding.

Contribution

It establishes the Dirichlet isospectral problem for non-obtuse trapezoids, demonstrating spectral uniqueness in this class of polygons.

Findings

Non-obtuse trapezoids are uniquely determined by their Dirichlet spectrum.

Extension of previous results from Neumann to Dirichlet spectrum.

Spectral geometry of trapezoids is now better understood.

Abstract

We show that non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum. This extends our previous result, which was only concerned with the Neumann Laplace spectrum.