The Santaló point for the Holmes-Thompson boundary area

Florent Nicolas Balacheff; Gil Solanes; Kroum Tzanev

doi:10.1016/j.aim.2021.108118

The Santaló point for the Holmes-Thompson boundary area

Florent Nicolas Balacheff, Gil Solanes, Kroum Tzanev

Research output: Contribution to journal › Article › Research › peer-review

Abstract

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.

Original language	English
Journal	Advances in Mathematics
DOIs	https://doi.org/10.1016/j.aim.2021.108118
Publication status	Published - 2022

Keywords

Convex body
Crofton formula
Holmes-Thompson area and volume
Minkowski geometry
Santaló point
Symplectic geometry

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10.1016/j.aim.2021.108118

https://ddd.uab.cat/record/250618

Invariantes locales y globales en geometria
Solanes Farres, G. (Principal Investigator), Balacheff , F. N. (Principal Investigator 2), Rubio Nuñez, R. (Collaborator), Gallego Gomez, E. (Investigator), Heusener, M. (Investigator), Marin Perez, D. (Investigator), Meersseman, L. (Investigator), Nicolau Reig, M. (Investigator), Porti Pique, J. (Investigator), Reventos Tarrida, A. (Investigator) & Mijares Verdú, S. (Collaborator)
Spanish Ministry of Science and Innovation
1/01/19 → 30/09/22
Project: Research Projects and Other Grants

Cite this

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title = "The Santal{\'o} point for the Holmes-Thompson boundary area",

abstract = "We explore the notion of Santal{\'o} 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 Santal{\'o} point expressed as an average of centroids of projections of the dual body.",

keywords = "Convex body, Crofton formula, Holmes-Thompson area and volume, Minkowski geometry, Santal{\'o} point, Symplectic geometry",

author = "Balacheff, {Florent Nicolas} and Gil Solanes and Kroum Tzanev",

year = "2022",

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language = "English",

journal = "Advances in Mathematics",

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AU - Balacheff, Florent Nicolas

AU - Solanes, Gil

AU - Tzanev, Kroum

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Convex body

KW - Crofton formula

KW - Holmes-Thompson area and volume

KW - Minkowski geometry

KW - Santaló point

KW - Symplectic geometry

U2 - 10.1016/j.aim.2021.108118

DO - 10.1016/j.aim.2021.108118

M3 - Article

SN - 0001-8708

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The Santaló point for the Holmes-Thompson boundary area

Abstract

Keywords

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Invariantes locales y globales en geometria

Cite this