The Santaló point for the Holmes-Thompson boundary area
We explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is C, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit bal...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:250618 |
| Acceso en línea: | https://ddd.uab.cat/record/250618 https://dx.doi.org/urn:doi:10.1016/j.aim.2021.108118 |
| Access Level: | acceso abierto |
| Palabra clave: | Convex body Crofton formula Holmes-Thompson area and volume Minkowski geometry Santaló point Symplectic geometry |
| Sumario: | We explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is C, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit ball, we exhibit a dual Santaló point expressed as an average of centroids of projections of the dual body. |
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