Isosystolic inequalities for optical hypersurfaces
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-di...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:287712 |
| Acceso en línea: | https://ddd.uab.cat/record/287712 https://dx.doi.org/urn:doi:10.1016/j.aim.2016.07.003 |
| Access Level: | acceso abierto |
| Palabra clave: | Convex geometry Finsler metric Geometry of numbers Mahler conjecture Optical hypersurface Systolic inequalities |
| Sumario: | 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. |
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