27 citations · 46 across the 9 of their papers we have counts for
4 papers · 1 filter
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…
Geometric invariants of fanning curves
Juan Carlos Álvarez Paiva, Carlos E. Durán
We study the geometry of an important class of generic curves in the Grassmannian manifolds of -dimensional subspaces and Lagrangian subspaces of under the action of th…
Dual mixed volumes and isosystolic inequalities
Juan Carlos Alvarez Paiva
The theory of dual mixed volumes is extended to star bodies in cotangent bundles and is used to prove several isosystolic inequalities for Hamiltonian systems and Finsler metrics.