Gardiner-Masur boundary of Teichmuller space : Vanishing subsurfaces and Uniquely ergodic boundary points

TL;DR

This paper explores the structure of the Gardiner-Masur boundary of Teichmuller space, comparing it with other compactifications, and characterizes boundary points related to uniquely ergodic measured foliations and mapping class group actions.

Contribution

It provides a geometric description of the Gardiner-Masur boundary, establishes its coincidence with the Thurston boundary at uniquely ergodic points, and analyzes the mapping class group action.

Findings

Coincidence of Gardiner-Masur and Thurston boundaries at uniquely ergodic points

Characterization of mapping class group elements by fixed points on the boundary

Geometric description comparing to Duchin-Leininger-Rafi compactification

Abstract

In this paper, we investigate the structure of the Gardiner-Masur boundary of Teichmuller space. Indeed, we will give a geometric description of boundary comparing to the Duchin-Leininger-Rafi compactification of the space of singular flat structures. We will obtain the coincidence between the Gardiner-Masur boundary and the Thurston boundary at the projective classes of uniquely ergodic measured foliations. We also study the action of the mapping class group on the Gardiner-Masur boundary and characterize the elements by fixed points. This paper has been withdrawn by the author. This paper will be renewal and the author will publish extended results elsewhere. If someone wants to see this preprint, please ask and consult the author.