Weil-Petersson geometry for families of hyperbolic conical Riemann Surfaces

TL;DR

This paper investigates the Weil-Petersson geometric structure on families of hyperbolic Riemann surfaces with conical singularities, focusing on the unique conical metric of constant negative curvature.

Contribution

It introduces a detailed analysis of Weil-Petersson geometry in the context of conical Riemann surfaces, extending classical results to singular metrics.

Findings

Characterization of Weil-Petersson metric for conical surfaces

Insights into the curvature properties of the moduli space

Extension of geometric structures to singular metrics

Abstract

We study the Weil-Petersson geometry for holomorphic families of Riemann Surfaces equipped with the unique conical metric of constant curvature -1.