Inverse mean curvature flow (IMCF) is a geometric flow that expands hypersurfaces by mean curvature. The flow has many geometric applications, especially to geometric inequalities, but a key obstacle to these is the formation of finite-time singularities. To deal with this, Huisken and Ilmanen developed a notion of weak solutions of IMCF which flow through these singularities and out to infinity. Weak IMCF is well-understood in Euclidean space, but much less is known about weak IMCF in hyperbolic space.

 

In this talk, I will present my recent work about regularity of weak IMCF in hyperbolic space, the key to which is an Alexandrov reflection method in the Poincare ball. Then I will apply these regularity results to extend two Minkowski inequalities for hypersurfaces in hyperbolic space. One of these inequalities implies a certain Penrose-type inequality in general relativity.

 

WebEx Link:https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=mc85ba49d60868ce76b75b170f1900e34

Meeting number (access code): 2523 415 8513

Meeting password: ZBfFJeaZ244

 

Organizers: Nicolau Sarquis Aiex (NTNU), Chung-Jun Tsai (NTU), Siao-Hao Guo (NTU)