The existence of singular isoperimetric hypersurfaces


Friday, January 12, 2024 - 13:00 to 13:50




Speaker: Dr. Gongping Niu (University of California San Diego) 

Title:The existence of singular isoperimetric hypersurfaces


It is well-known that isoperimetric hypersurfaces in a smooth, compact (n+1)-manifold are smooth up to a closed set of codimension at least 7. We prove that the dimension estimate of singularities is sharp. In this talk, we will explore an example of an 8-dimensional closed smooth Riemannian manifold, whose unique isoperimetric region, with half the volume of the manifold, displays two isolated singularities on its boundary. Furthermore, for n > 7, we utilize similar methods to construct singular isoperimetric hypersurfaces in higher dimensions.


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