Min CHEN, U. of Oregon
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PDL C-401
The geometric flow of hypersurfaces is an interesting and active area. Its importance lies in the applications in geometry and topology. For example, Huisken and Ilmanen in 2001 applied the inverse mean curvature flow to prove the famous Penrose conjecture; applying the inverse curvature flow, Guan and Li in 2009 proved the Alexandrov-Fenchel inequalities for star-shaped and $k$-convex domains in Euclidean space. Brendle-Guan-Li proposed a conjecture on the Alexandrov-Fenchel inequalities for hypersurface in the sphere and introduced a locally constrained fully nonlinear curvature flow to study this conjecture. In this talk, we will discuss using a new flow type to study this question and some new progress in this conjecture.