78 citations · 201 across the 31 of their papers we have counts for
38 papers
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…
Operations on constructible functions and generalized valuations
Andreas Bernig, Vadim Lebovici
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures.…
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…
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…
The Weyl tube theorem for Kähler manifolds
Andreas Bernig, Joseph H. G. Fu, Gil Solanes +1
As sharpened in terms of Alesker's theory of valuations on manifolds, a classic theorem of Weyl asserts that the coefficients of the tube polynomial of an isometrically embedded ri…
Crofton formulas in pseudo-Riemannian space forms
Andreas Bernig, Dmitry Faifman, Gil Solanes
Crofton formulas on simply-connected Riemannian space forms allow to compute the volumes, or more generally the Lipschitz-Killing curvature integrals of a submanifold with corners,…