Geodesics on weighted projective spaces

TL;DR

This paper investigates the inverse spectral problem for weighted projective spaces, demonstrating that wave-trace methods can often determine the weights of these spaces from spectral data.

Contribution

It introduces wave-trace techniques to recover weights of weighted projective spaces, advancing understanding of spectral geometry in these spaces.

Findings

Weights can often be determined from spectral data

Wave-trace methods are effective for inverse problems

Spectral data encodes geometric information

Abstract

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can "hear" the weights of a weighted projective space.