14 citations · 15 across the 2 of their papers we have counts for
3 papers
math.DG2010★ 14 cited
Finsler surfaces with prescribed geodesics
Juan-Carlos Álvarez-Paiva, Gautier Berck
We construct all Finsler metrics on the two-sphere for which geodesics are circles and show that any (reversible) path geometry on a two-dimensional manifold is locally the system…
math.DG2008
Volume entropy of Hilbert Geometries
Gautier Berck, Andreas Bernig, Constantin Vernicos
It is shown that the volume entropy of a Hilbert geometry associated to an -dimensional convex body of class equals . To achieve this result, a new projective inv…
math.DG2004★ 1 cited
What is wrong with the Hausdorff measure in Finsler spaces
Juan Carlos Alvarez Paiva, Gautier Berck
We construct a class of Finsler metrics in three-dimensional space such that all their geodesics are lines, but not all planes are extremal for their Hausdorff area functionals. Th…