35 citations · 58 across the 15 of their papers we have counts for
24 papers
Translation invariant curvature measures of convex bodies
Jakob Schuhmacher, Thomas Wannerer
In a series of papers, Weil initiated the investigation of translation invariant curvature measures of convex bodies, which include as prime examples Federer's curvature measures.…
An Intersection Product for the Polytope Algebra
Thomas Wannerer
We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product,…
Complex and Quaternionic Analogues of Busemann's Random Simplex and Intersection Inequalities
Christos Saroglou, Thomas Wannerer
In this paper, we extend two celebrated inequalities by Busemann -- the random simplex inequality and the intersection inequality -- to both complex and quaternionic vector spaces.…
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 Fourier transform on valuations is the Fourier transform
Dmitry Faifman, Thomas Wannerer
Alesker has proved the existence of a remarkable isomorphism of the space of translation-invariant smooth valuations that has the same functorial properties as the classical Fourie…
Dually Lorentzian Polynomials
Julius Ross, Hendrik Süß, Thomas Wannerer
We introduce and study a notion of dually Lorentzian polynomials, and show that if is non-zero and dually Lorentzian then the operator \[s(\partial_{x_1},\ldots,\partial_{x_n})…