Gluing methods for geometric PDE

Prof. Nicos Kapouleas (Brown University)

Tuesday, November 13, 13:00 - 15:00, HG G 19.1
Thursday, November 15, 13:00 - 15:00, HG G 43
Thursday, November 22, 13:00 - 15:00, HG G 43

Abstract

The purpose of this minicourse is to present a methodology for a class of gluing constructions in Differential Geometry and its application to various problems. This methodology originates from a construction of Constant Scalar Curvature metrics by R. Schoen and Constant Mean Curvature surfaces by the author, and it was refined and systematized in a gluing construction for Wente tori where a "Geometric Principle'" guiding the organization of the construction was proposed. In the introduction I will discuss the problems to which this methodology has been applied and related geometric questions. I will outline then in detail some applications emphasizing differences and similarities in the various problems. In particular I will discuss constructions of Special Lagrangian cones and CMC surfaces, doubling constructions for minimal surfaces, and desingularization constructions for minimal surfaces.