4 papers
The Faber-Krahn position of convex bodies and Gaussian measure inequalities
Dmitry Faifman, Iosif Polterovich
We say that a convex body is in Faber-Krahn position if it minimizes the first Dirichlet eigenvalue within its volume-preserving linear orbit. We prove that this position is unique…
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…
Convex valuations, from Whitney to Nash
Dmitry Faifman, Georg C. Hofstätter
We consider the Whitney problem for valuations: does a smooth -homogeneous translation-invariant valuation on exist that has given restrictions to a fixed family $…