27 citations · 46 across the 9 of their papers we have counts for
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math.SG2004★ 3 cited
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.
math.MG2004★ 1 cited
Dual spheres have the same girth
Juan Carlos Alvarez Paiva
Symplectic and Finsler geometry are used to settle a conjecture of Schäffer stating that the girth of a normed space--the infimum of the lengths of all closed, rectifiable, central…
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…