Room 440, Astronomy-Mathematics Building, NTU + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學天文數學館440室 + Cisco WebEx)
Weak Inverse Mean Curvature Flow and Minkowski Inequalities in Hyperbolic Space
Brian Harvie (NCTS)
Abstract
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.
Meeting number (access code): 2523 415 8513
Meeting password: ZBfFJeaZ244
Organizers: Nicolau Sarquis Aiex (NTNU), Chung-Jun Tsai (NTU), Siao-Hao Guo (NTU)
