All Teichmuller spaces are not starlike

TL;DR

This paper completes the proof regarding the non-starlikeness of finite-dimensional Teichmuller spaces within Bers' embedding, addressing a longstanding problem in complex analysis and Teichmuller theory.

Contribution

It finalizes the proof that all finite-dimensional Teichmuller spaces are not starlike in Bers' embedding, resolving a key open problem.

Findings

Finite-dimensional Teichmuller spaces are not starlike in Bers' embedding.

The proof completes the understanding of the geometric structure of Teichmuller spaces.

Addresses the case of punctured Riemann surfaces with positive dimension.

Abstract

This paper is the final step in solving the problem of starlikeness of Teichmuller spaces in Bers' embedding. This step concerns the case of finite dimensional Teichmuller spaces ${\mathbf T}(g, n)$ of positive dimension (corresponding to punctured Riemann surfaces of finite conformal type $(g, n)$ with $2g - 2 + n > 0$).