Description
In this talk, we will discuss the isoperimetric inequality and its high-order version -- Alexandrov-Fenchel inequality, which dates back to Queen Dido in the ancient Carthage era. We introduce the quermassintegrals for compact hypersurfaces with capillary boundary from the variational viewpoint. Then by using a constrained mean curvature type flow, we can obtain some new isoperimetric type inequalities for compact hypersurfaces with capillary boundary.
