Extremal problems for the central projection

Shigehiro Sakata

Research output: Contribution to journalArticle

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

Fingerprint

Extremal Problems
Tangent plane
Projection
Closed
Subset
Minimality
Unit Sphere
Uniqueness
Minimise

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Extremal problems for the central projection. / Sakata, Shigehiro.

In: Journal of Geometry, Vol. 103, No. 1, 04.2012, p. 125-129.

Research output: Contribution to journalArticle

Sakata, Shigehiro. / Extremal problems for the central projection. In: Journal of Geometry. 2012 ; Vol. 103, No. 1. pp. 125-129.
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