Abstract: The weak inverse mean curvature flow, initially introduced by Huisken and Ilmanen, has been a powerful tool in approaching scalar curvature problems. In recent years, on the other hand, the analytic and measure-theoretic structure of the inverse mean curvature flow itself has drawn growing attention. In this talk, I will introduce a new theory for the (weak) inverse mean curvature flow inside bounded domains. In our setting, the boundary of the domain plays the role of an outer obstacle, and the hypersurfaces in the flow stick tangentially to the boundary upon contact. We will discuss the relevant motivations for considering such a problem, as well as the analytic/geometric behaviors of the solutions. Then we will explain an existence and C^(1,α) regularity theorem for smooth boundary, and the ideas involved.

Biography: Kai Xu is currently a fourth-year graduate student at Duke University, under the supervision of Prof. Hubert Bray. His research is focused in the areas of scalar curvature and inverse mean curvature flow.

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