Uniformization of Surfaces with Conical Singularities
Channel: UMD Mathematics
Date: 2013-04-23

Andrea Malchiodi
Professor of Mathematics
The University of Warwick

ABSTRACT

We consider a class of singular Liouville equations which arise from the problem of prescribing the Gaussian curvature of a surface imposing a given conical structure at a finite number of points (as well as from models in Chern-Simons theory). The problem is variational, and differently from the "regular" case the Euler-Lagrange functional might be unbounded from below. We will look for critical points of saddle type using a combination of improved geometric inequalities and topological methods. This is joint work with D. Bartolucci, A. Carlotto, F. De Marchis and D. Ruiz.

Recorded April 13th, 2013 at Calabifest: The 28th Geometry Festival.