Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
In this paper we first introduce quermassintegrals for free boundary hypersurfaces in the $(n+1)$-dimensional Euclidean unit ball. Then we solve some related isoperimetric type problems for convex free boundary hypersurfaces, which lead to new Alexandrov-Fenchel inequalities. In particular, for $n=2$ we obtain a Minkowski-type inequality and for $n=3$ we obtain …