Estimates of the Bergman kernel on Teichmuller space

TL;DR

This paper compares the Bergman kernel form with the pushforward of the Masur-Veech measure on Teichmuller space, providing insights into their relationship for genus g≥2.

Contribution

It offers a novel comparison between the Bergman kernel form and Masur-Veech measure pushforward on Teichmuller space for higher genus surfaces.

Findings

Established a relationship between the Bergman kernel and Masur-Veech measure

Provided explicit comparisons for genus g≥2

Enhanced understanding of geometric structures on Teichmuller space

Abstract

In this paper, a comparison between the Bergman kernel form and the pushforward measure of the Masur-Veech meaure on the Teichmuller space of genus $g\ge 2$ is obtained.