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math.MG2022
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…
math.DG2022
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…
math.DG2022★ 2 cited
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…