The Carath\'eodory Metric on Finite Dimensional Teichm\"uller Spaces: A property of the Maskit coordinates

TL;DR

This paper demonstrates the existence of new one-dimensional subspaces in finite-dimensional Teichmüller spaces where the Carathéodory and Kobayashi metrics coincide, using Maskit coordinates.

Contribution

It introduces novel families of subspaces in Teichmüller space where these metrics agree, leveraging Maskit coordinates.

Findings

Existence of new one-dimensional subspaces with metric equality

Use of Maskit coordinates to analyze Teichmüller space

Advancement in understanding metric properties in Teichmüller theory

Abstract

Using the Maskit coordinates for Teichmuller space, we prove the existence of new families of one dimensional subspaces on which the Caratheodory and Kobayashi metrics agree.