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.
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Sakata, S.: Extremal problems for the solid angle. arXiv:1103.1727
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Sakata, S. Extremal problems for the central projection. J. Geom. 103, 125–129 (2012). https://doi.org/10.1007/s00022-012-0113-7
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DOI: https://doi.org/10.1007/s00022-012-0113-7