Lipschitz Constants To Curve Complexes For Punctured Surfaces

TL;DR

This paper establishes asymptotic bounds for the Lipschitz constants of the systole map from Teichmuller space to the curve complex, extending known results to punctured surfaces with fixed genus or rational genus-to-puncture ratios.

Contribution

It provides new asymptotic bounds for Lipschitz constants in the context of punctured surfaces, generalizing previous results for closed surfaces.

Findings

Asymptotic bounds for Lipschitz constants derived

Results applicable to fixed genus and rational genus-puncture ratios

Extension of known bounds from closed to punctured surfaces

Abstract

We give asymptotic bounds for the optimal Lipschitz constants for the systole map from the Teichmuller space to the curve complex. We give similar results to those known for closed surfaces in the cases when the genus is fixed or the ratio of genus and punctures is a rational number.