In this paper, we establish some sharp inequalities between the volume and the integral of the kth mean curvature for (k+1)-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.
|Original language||English (US)|
|Number of pages||26|
|Journal||International Mathematics Research Notices|
|State||Published - Jan 1 2014|
All Science Journal Classification (ASJC) codes