Liangjun Weng (Rom):
Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
Time and place
Tuesday, 17.10.23, 16:00-17:00, Raum 127, Ernst-Zermelo-Str. 1
Abstract
Let \(\bSigma\) be a compact hypersurface with a capillary boundary in a unit ball, in this talk, I will discuss the relative isoperimetric problem for such kinds of hypersurfaces. We introduce the relative quermassintegrals for such hypersurfaces from the variational viewpoint. Then by introducing some constrained nonlinear curvature flows, which preserve one geometric quantity invariant and monotone increase another, we obtain the Alexandrov-Fenchel inequality for such hypersurfaces. The talk is based on joint work with Profs. Guofang Wang and Chao Xia.\n