Extremal problems for the central projection

Shigehiro Sakata

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider area minimizing problems for the image of a closed subset in the unit sphere under a projection from the center of the sphere to a tangent plane, the central projection. We show, for any closed subset in the sphere, the uniqueness of a tangent plane that minimizes the area, and then the minimality of the spherical discs among closed subsets with the same spherical area.

Original languageEnglish
Pages (from-to)125-129
Number of pages5
JournalJournal of Geometry
Volume103
Issue number1
DOIs
Publication statusPublished - 2012 Apr
Externally publishedYes

Keywords

  • Central projection
  • extremal problem
  • gnomonic projection
  • polar set

ASJC Scopus subject areas

  • Geometry and Topology

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