The Santaló point for the Holmes-Thompson boundary area

The Santaló point for the Holmes-Thompson boundary area

Altres ajuts: acords transformatius de la UAB 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...

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Bibliographische Detailangaben
Hauptverfasser: Balacheff, Florent Nicolas, Solanes, Gil, Tzanev, Kroum
Format: Artikel
Sprache:eng
Schlagworte:
Convex body
Crofton formula
Holmes-Thompson area and volume
Minkowski geometry
Santaló point
Symplectic geometry
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Zusammenfassung:Altres ajuts: acords transformatius de la UAB 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.