46 citations · 50 across the 9 of their papers we have counts for
12 papers
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…
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…
Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations
Andreas Bernig, Jan Kotrbatý, Thomas Wannerer
The algebra of smooth translation-invariant valuations on convex bodies, introduced by S.Alesker in the early 2000s, was in part proved and in part conjectured to satisfy propertie…
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…
From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
Jan Kotrbatý, Thomas Wannerer
The Alesker-Bernig-Schuster theorem asserts that each irreducible representation of the special orthogonal group appears with multiplicity at most one as a subrepresentation of the…
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…
Magnetic field distribution in magnetars
Debarati Chatterjee, Jerome Novak, Micaela Oertel
Using an axisymmetric numerical code, we perform an extensive study of the magnetic field configurations in non-rotating neutron stars, varying the mass, magnetic field strength an…