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Every convex body has a unique illuminating center

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Abstract

We investigate the strict power concavity of the convolution of a function and the characteristic function of a convex body. Using the result, we show that every convex body has a unique illuminating center.

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Authors and Affiliations

  1. Faculty of Education, University of Miyazaki, 1-1, Gakuen Kibanadai West, Miyazaki, Miyazaki, 889-2192, Japan

    Shigehiro Sakata

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  1. Shigehiro Sakata
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Correspondence to Shigehiro Sakata.

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Sakata, S. Every convex body has a unique illuminating center. J. Geom. 108, 655–662 (2017). https://doi.org/10.1007/s00022-016-0365-8

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  • DOI: https://doi.org/10.1007/s00022-016-0365-8

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