Volume entropy of Hilbert geometries

A Measure of Maximal Entropy for Nonuniformly Hyperbolic Hilbert Geometries

Isometries of polyhedral Hilbert geometries

We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n ≥ 2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex for all n ≥ 2, and find that it has the collineation group as an index-two subgroup. These results confirm, for the class of pol...

On Rough-isometry Classes of Hilbert Geometries

We prove that Hilbert geometries on uniformly convex Euclidean domains with C 2-boundaries are roughly isometric to the real hyperbolic spaces of corresponding dimension.

Topological Dynamics of Nonstrictly Convex Hilbert Geometries

Microstate Geometries and Entropy Enhancement

In string theory, black-hole backgrounds are far from unique and there are large families of completely smooth, horizonless geometries with the same structure as a black hole from infinity down to the neighborhood of the black-hole horizon. These microstate geometries cap off in foam of topological bubbles. I review some of the recent progress in constructing these smooth horizonless geometries...