Analysis Seminar

SPEAKER: Matthew Romney (Stony Brook University)

TITLE: Polyhedral approximation and uniformization of metric surfaces

ABSTRACT: We prove that arbitrary surfaces with a length metric can be approximated in the Gromov--Hausdorff sense by polyhedral surfaces with controlled geometry. One of the main tools, of independent interest, is a recent result on decomposing metric surfaces into convex triangles. We then apply our approximation theorem to the uniformization problem for metric surfaces, which asks for the existence of local quasiconformal parametrizations by a domain in the Euclidean plane. This talk covers joint work with Paul Creutz and Dimitrios Ntalampekos.