Torsional rigidity and isospectral planar sets

TL;DR

This paper demonstrates that torsional rigidity can distinguish between certain pairs of isospectral planar sets, providing a new method to differentiate shapes with identical spectral properties.

Contribution

It introduces the use of torsional rigidity as a distinguishing invariant for isospectral planar sets, which was not previously established.

Findings

Torsional rigidity can differentiate specific isospectral pairs.

Isospectral sets can have different torsional rigidity values.

The method offers a new approach to shape analysis in spectral geometry.

Abstract

We prove that a certain pair of isospectral planar sets are distinguished by torsional rigidity.