24 citations · 30 across the 8 of their papers we have counts for
8 papers
When is a Minkowski norm strictly sub-convex?
Stéphane Simon, Patrick Verovic
The aim of this paper is to give two complete and simple characterizations of Minkowski norms N on an arbitrary topological real vector space such that the sublevel sets of N are s…
Functions with strictly convex epigraph
Stéphane Simon, Patrick Verovic
The aim of this paper is to provide a complete and simple characterization of functions with domain in a topological real vector space whose epigraph is strictly convex.
Laplacian and spectral gap in regular Hilbert geometries
Thomas Barthelmé, Bruno Colbois, Mickaël Crampon +1
We study the spectrum of the Finsler--Laplace operator for regular Hilbert geometries, defined by convex sets with boundaries. We show that for an -dimensional geometry, t…
Two properties of volume growth entropy in Hilbert geometry
Bruno Colbois, Patrick Verovic
The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-p…
Hilbert geometry for convex polygonal domains
Bruno Colbois, Constantin Vernicos, Patrick Verovic
We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane.
Hilbert domains quasi-isometric to normed vector spaces
Bruno Colbois, Patrick Verovic
We prove that a Hilbert domain which is quasi-isometric to a normed vector space is actually a convex polytope.