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math.DG2013★ 27 cited
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…
math.DG2013★ 7 cited
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…