DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, October 4 Padelford C-36 3:45 PM

An “end-to-end” gluing construction for surfaces of constant mean curvature

Jesse Ratzkin (UW)

Noncompact embedded surfaces of finite topological type with constant mean curvature (CMC surfaces) have a precise asymptotic structure. This allows one to patch together two CMC surfaces along their ends (provided the asymptotics match) and obtain a new surface whose mean curvature is almost constant. The problem of deforming such a surface (an “approximate solution”) to a exact CMC surface involves solving a quasilinear elliptic PDE. The purpose of this talk is to describe how one constructs such approximate solutions and how one can perturb them into exact solutions.