Title :

Isosystolic inequalities for optical hypersurfaces

Author(s) :

Álvarez Paiva, Juan-Carlos [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Balacheff, Florent [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Tzanev, Kroum [Auteur]

English keyword(s) :

Systolic inequalities
optical hypersurface
Finsler metric
geometry of numbers
convex geometry
Mahler conjecture

HAL domain(s) :

Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Géométrie métrique [math.MG]
Mathématiques [math]/Géométrie symplectique [math.SG]

English abstract : [en]

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 geometry of numbers. In particular, we show that ...
Show more >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 geometry of numbers. In particular, we show that if an optical hypersurface of contact type in the cotangent bundle of the 2-dimensional torus encloses a volume $V$, then it carries a periodic characteristic whose action is at most $\sqrt{V/3}$. This result is deduced from an interesting dual version of Minkowski's lattice-point theorem: if the origin is the unique integer point in the interior of a planar convex body, the area of its dual body is at least 3/2.Show less >

Language :

Anglais

ANR Project :

Géométrie de Finsler et applications

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL