3 papers
math.DG2020
A Funk perspective on billiards, projective geometry and Mahler volume
Dmitry Faifman
We explore connections furnished by the Funk metric, a relative of the Hilbert metric, between projective geometry, billiards, convex geometry and affine inequalities. We first sho…
math.DG2019
The Weyl principle on the Finsler frontier
Dmitry Faifman, Thomas Wannerer
Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz-Killing valuations. They d…
math.DG2013
Convex valuations invariant under the Lorentz group
Semyon Alesker, Dmitry Faifman
We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuati…