Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665064 | Advances in Mathematics | 2016 | 39 Pages |
Abstract
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 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
J.C. Álvarez Paiva, F. Balacheff, K. Tzanev,