4 papers
Godbersen's conjecture and the -Rogers-Shephard inequality
Jan Kotrbatý, Mohamed A. Mouamine
We prove that the mixed volume of a convex body with its reflection about the origin is maximized by simplices. This confirms a conjecture of C. Godbersen from 1938 and refines the…
The volume of tubes in Lie groups
Andreas Bernig, Dmitry Faifman, Jan Kotrbatý
The problem of computing the volume of tubes in riemannian manifolds goes back to Weyl and Hotelling. Here we find explicit Taylor series for the volume of a tube in a Lie group eq…
Invariant valuations on Lie groups
Andreas Bernig, Dmitry Faifman, Jan Kotrbatý
Convolution of valuations was introduced by the first named author and Fu for linear spaces, and later by Alesker and the first named author for compact Lie groups. In this paper w…
On a generalization of Godbersen's conjecture
Jan Kotrbatý
The long-standing Godbersen's conjecture asserts that the Rogers-Shephard inequality for the volume of the difference body is refined by an inequality for the mixed volume of a con…