46 citations · 50 across the 9 of their papers we have counts for
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Higher-order Godbersen inequality and a characterization of simplices via the face lattice
Filip Fryš, Jan Kotrbatý, Mohamed A. Mouamine +1
We settle the long-standing Godbersen conjecture that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized precisely by simp…
Around higher-order Godbersen conjectures
Filip Fryš, Jan Kotrbatý
We consider two higher-order generalizations of the Godbersen conjecture for mixed volumes of convex bodies, which were first proposed by Schneider in 2000. First, we establish the…
Godbersen's conjecture and the -Rogers-Shephard inequality
Jan Kotrbatý, Mohamed A. Mouamine
We prove that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized by simplices. This confirms a conjecture of C. Godbersen…
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…
Integral geometry on the octonionic plane
Jan Kotrbatý, Thomas Wannerer
We describe explicitly the algebra of Spin(9)-invariant, translation-invariant, continuous valuations on the octonionic plane. Namely, we present a basis in terms of invariant diff…
On mixed Hodge-Riemann relations for translation-invariant valuations and Aleksandrov-Fenchel inequalities
Jan Kotrbatý, Thomas Wannerer
A version of the Hodge-Riemann relations for valuations was recently conjectured and proved in several special cases by the first-named author. The Lefschetz operator considered th…
On Hodge-Riemann relations for translation-invariant valuations
Jan Kotrbatý
The Alesker product turns the space of smooth translation-invariant valuations on convex bodies into a commutative associative unital algebra, satisfying Poincaré duality and the h…