The length spectrum of holomorphic quadratic differential metrics

TL;DR

This paper proves that on closed surfaces, flat metrics from holomorphic quadratic differentials can be uniquely identified by their length spectrum, distinguishing them from other flat cone metrics.

Contribution

It establishes a spectral characterization of holomorphic quadratic differential metrics among all flat cone metrics on closed surfaces.

Findings

Holomorphic quadratic differential metrics are uniquely determined by their length spectrum.

The result distinguishes these metrics from other flat cone metrics.

Provides a spectral criterion for identifying holomorphic quadratic differential metrics.

Abstract

In this paper we prove that on a closed oriented surface, flat metrics determined by holomorphic quadratic differentials can be distinguished from other flat cone metrics by the length spectrum.