Abstract: The Teichmüller space of a closed set in the Riemann sphere is a simply connected complex Banach manifold. We will discuss some conformal naturality properties of such Teichmüller spaces, and some other analytic properties. For applications, we will use these Teichm¨uller spaces to give an explicit example of a maximal holomorphic motion, and discuss holomorphic families of Jordan curves. As a comparison, we will mention an example of Hubbard on holomorphic motions, based on his famous theorem on the non-existence of holomorphic sections for Teichmüller curves. If time permits, we will include a brief discussion on holomorphic families of Riemann surfaces. Parts of this talk will be based on some previous works with Yunping Jiang and Hiroshige Shiga, and a more recent work with Xinlong Dong and Arshiya Farhath. G.
Zoom Meeting ID: 181 155 584
