Uploaded April 2026 | Updated September 2026, 2 weeks ago
The (weak) inverse mean curvature flow is known as a useful tool for studying the geometry of scalar curvature. In recent work with Otis Chodosh and Yi Lai, we used this tool to prove that complete contractible PSC 3-manifolds with bounded geometry are diffeomorphic to $\mathbb{R}^3$. In this talk, we will investigate the analytic side of this theory. We will discuss the existence and properties of the desirable class of solutions -- which are usually called the innermost inverse mean curvature flow. When being run in the interior of a smooth domain, this class of solutions has the geometric meaning that all hypersurfaces stay tangential to the boundary. We will also discuss its relation to p-harmonic functions with Dirichlet boundary condition.
Kai Xu (Berkeley)
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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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The (weak) inverse mean curvature flow is known as a useful tool for studying the geometry of scalar curvature. In recent work with Otis Chodosh and Yi Lai, we used this tool to prove that complete contractible PSC 3-manifolds with bounded geometry are diffeomorphic to $\mathbb{R}^3$. In this talk, we will investigate the analytic side of this theory. We will discuss the existence and properties of the desirable class of solutions -- which are usually called the innermost inverse mean curvature flow. When being run in the interior of a smooth domain, this class of solutions has the geometric meaning that all hypersurfaces stay tangential to the boundary. We will also discuss its relation to p-harmonic functions with Dirichlet boundary condition.
Kai Xu (Berkeley)
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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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