| Abstract: | In this talk, we will discuss the relative Alexandrov-Fenchel inequality. Firstly we introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball and derive its first variational formula. Then by using a locally constrained nonlinear curvature flow, which preserves the n-th quermassintegral and non-decreases the k-th quermassintegral, we obtain the Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in unit ball. This talk is based on the recent joint work with Prof. Chao XIA. |
