On Infinitesimal Strebel Points

TL;DR

This paper proves that on any infinite-type Riemann surface, every Teichmüller space element has an equivalent infinitesimal Strebel point, advancing understanding of the structure of Teichmüller spaces.

Contribution

It establishes the existence of infinitesimal Strebel points within the Teichmüller space of infinite-type Riemann surfaces, a previously unresolved question.

Findings

Existence of infinitesimal Strebel points in infinite-type cases

Extension of Strebel theory to infinite Riemann surfaces

New insights into the geometry of Teichmüller spaces

Abstract

In this paper, we prove that if $X$ is a Riemann surface of infinite analytic type and $[\mu ]_T$ is any element of Teichm\"uller space, then there exists $\mu_1 \in [\mu]_T$ so that $\mu_1$ is an infinitesimal Strebel point.