Extremal problems for the central projection

Shigehiro Sakata

doi:10.1007/s00022-012-0113-7

Extremal problems for the central projection

Shigehiro Sakata^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	125-129
Number of pages	5
Journal	Journal of Geometry
Volume	103
Issue number	1
DOIs	https://doi.org/10.1007/s00022-012-0113-7
Publication status	Published - 2012 Apr
Externally published	Yes

Keywords

Central projection
extremal problem
gnomonic projection
polar set

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s00022-012-0113-7

Cite this

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title = "Extremal problems for the central projection",

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.",

keywords = "Central projection, extremal problem, gnomonic projection, polar set",

author = "Shigehiro Sakata",

year = "2012",

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AB - 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.

KW - Central projection

KW - extremal problem

KW - gnomonic projection

KW - polar set

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Extremal problems for the central projection

Abstract

Keywords

ASJC Scopus subject areas

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