10 papers
A reverse isoperimetric inequality in three-dimensional space forms
Kostiantyn Drach, Gil Solanes, Kateryna Tatarko
A -convex body in a three-dimensional space form of constant curvature is a compact convex set whose boundary has normal curvatures bounded below b…
Projective transformations of convex bodies and volume product
Florent Balacheff, Gil Solanes, Kroum Tzanev
In this paper we study certain variational aspects of the volume product functional restricted to the space of small projective deformations of a fixed convex body. In doing so, we…
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…
Crofton formulas in pseudo-Riemannian space forms
Andreas Bernig, Dmitry Faifman, Gil Solanes
Crofton formulas on simply-connected Riemannian space forms allow to compute the volumes, or more generally the Lipschitz-Killing curvature integrals of a submanifold with corners,…
The Santaló point for the Holmes-Thompson boundary area
Florent Balacheff, Gil Solanes, Kroum Tzanev
We explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is , and in the case where unit bal…
Uniqueness of curvature measures in pseudo-Riemannian geometry
Andreas Bernig, Dmitry Faifman, Gil Solanes
The recently introduced Lipschitz-Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that th…