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Characterization of balls by generalized Riesz energy

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  • Jun O'Hara

Abstract

We show that balls, circles and 2‐spheres can be identified by generalized Riesz energy among compact submanifolds of the Euclidean space that are either closed or with codimension 0, where the Riesz energy is defined as the double integral of some power of the distance between pairs of points. As a consequence, we obtain the identification by the interpoint distance distribution.

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  • Jun O'Hara, 2019. "Characterization of balls by generalized Riesz energy," Mathematische Nachrichten, Wiley Blackwell, vol. 292(1), pages 159-169, January.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:1:p:159-169
    DOI: 10.1002/mana.201700256
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