Xin Zhou: Mean Curvature and Variational Theory

Mathematical models of soap bubbles and capillary surfaces are described by a class of prescribing mean curvature (PMC) equations. Minimal surfaces and constant mean curvature (CMC) surfaces are special classes of PMC surfaces. In variational theory, PMC surfaces are stationary points of the area functional plus a volume-related term. In this talk, we will survey recent developments of the existence theory of such surfaces, including the min-max theory for CMC/PMC surfaces and a Morse theory for area functional. In particular, we will explain our recent solution of the Multiplicity One Conjecture for minimal surfaces using the PMC min-max theory.
Slides: www.mathunion.org/fileadmin/I...