Geometry, Topology and Dynamics Seminar
David Dumas
UIC
Epstein surfaces, trees, and bubbles
Abstract: We will discuss a construction of C. Epstein that relates conformal metrics on planar domains to locally convex surfaces in hyperbolic space, and an application of this construction to complex projective structures.
In this application we describe the limit R-tree of a sequence of holonomy representations of projective structures on a fixed Riemann surface X. By choosing an appropriate family of conformal metrics, a divergent sequence of projective structures gives rise to a family of parameterized surfaces in hyperbolic space. Analyzing this family of surfaces, we find that they develop a finite set of "bubbles", and that after removing these, the rest of the surface converges to (after rescaling) to the limit R-tree.
Monday February 2, 2009 at 3:00 PM in SEO 612