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math.DG2026
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…
math.DG2025
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…
math.DG2025
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 $…