Date of Degree
Teichmüller space of a closed set, Teichmüller contraction, Holomorphic isometries, Schwarz's lemma, Complex geodesics
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).
Chatterjee, Nishan, "Some Metric Properties of the Teichmüller Space of a Closed Set in the Riemann Sphere" (2017). CUNY Academic Works.