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比利时vs摩洛哥足彩
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比利时vs摩洛哥足彩
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university of california san diego
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postdoc seminar
gongping niu
ucsd
the existence of singular isoperimetric hypersurfaces
abstract:
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.
november 30, 2023
3:00 pm
apm 5829
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