Date of Degree

9-2017

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Yunping Jiang

Advisor

Sudeb Mitra

Committee Members

Ara Basmajian

Yunping Jiang

Linda Keen

Sudeb Mitra

Subject Categories

Analysis

Keywords

Teichmüller space of a closed set, Teichmüller contraction, Holomorphic isometries, Schwarz's lemma, Complex geodesics

Abstract

Let E be an infinite closed set in the Riemann sphere, and let T(E) denote its Teichmüller space. In this dissertation we study some metric properties of T(E). We prove Earle's form of Teichmüller contraction for T(E), holomorphic isometries from the open unit disk into T(E), extend Earle's form of Schwarz's lemma for classical Teichmüller spaces to T(E), and finally study complex geodesics and unique extremality for T(E).

Included in

Analysis Commons

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