Isospectral Alexandrov Spaces

TL;DR

This paper presents the first known examples of compact Alexandrov spaces that are isospectral but not isometric, extending previous work with a new construction method.

Contribution

It introduces a novel construction of non-isometric Alexandrov spaces that are isospectral, generalizing earlier results using the torus method.

Findings

First non-trivial examples of isospectral non-isometric Alexandrov spaces

Extension of previous methods to Alexandrov spaces

Demonstrates diversity of spectral geometry beyond Riemannian orbifolds

Abstract

We construct the first non-trivial examples of compact non-isometric Alexandrov spaces which are isospectral with respect to the Laplacian and not isometric to Riemannian orbifolds. This construction generalizes independent earlier results by the authors based on Schueth's version of the torus method.