27 citations · 46 across the 9 of their papers we have counts for
11 papers
Rigidity results for geodesically reversible Finsler metrics
Juan-Carlos Alvarez Paiva
A Finsler metric is geodesically reversible if geodesics remain geodesics after a change of orientation. Asymmetric norms on vector spaces and Funk metrics in the interior of conve…
Periodic Solutions of Hilbert's Fourth Problem
Juan-Carlos Álvarez Paiva, José Barbosa Gomes
It is shown that a possibly irreversible Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat me…
Isosystolic inequalities for optical hypersurfaces
Juan-Carlos Alvarez Paiva, Florent Balacheff, Kroum Tzanev
We explore a natural generalization of systolic geometry to Finsler metrics and optical hypersurfaces with special emphasis on its relation to the Mahler conjecture and the geometr…
Asymmetry in Hilbert's fourth problem
Juan-Carlos Alvarez Paiva
In the asymmetric setting, Hilbert's fourth problem asks to construct and study all (non-reversible) projective Finsler metrics: Finsler metrics defined on open, convex subsets of…
Contact geometry and isosystolic inequalities
Juan-Carlos Alvarez Paiva, Florent Balacheff
A long-standing open problem in systolic geometry asks whether a Riemannian metric on the real projective space whose volume equals that of the canonical metric, but is not isometr…
Optimalité systolique infinitésimale de l'oscillateur harmonique
Juan-Carlos Álvarez Paiva, Florent Balacheff
We study the infinitesimal aspects of the following problem. Let H be a Hamiltonian of \R^{2n} whose energy surface {H=1} encloses a compact starshaped domain of volume equal to th…