The Santaló point for the Holmes-Thompson boundary area

Florent Balacheff*, Gil Solanes, Kroum Tzanev

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-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 C1, 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 languageEnglish
Article number108118
JournalAdvances in Mathematics
DOIs
Publication statusPublished - 1 Nov 2021

Keywords

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

Fingerprint

Dive into the research topics of 'The Santaló point for the Holmes-Thompson boundary area'. Together they form a unique fingerprint.

Cite this