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Regularized Riesz energies of submanifolds

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  • Jun O'Hara
  • Gil Solanes

Abstract

Given a closed submanifold, or a compact regular domain, in Euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs of points. When this integral diverges, we compare two different regularization techniques (Hadamard's finite part and analytic continuation), and show that they give essentially the same result. We prove that some of these energies are invariant under Möbius transformations, thus giving a generalization to higher dimensions of the Möbius energy of knots.

Suggested Citation

  • Jun O'Hara & Gil Solanes, 2018. "Regularized Riesz energies of submanifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 291(8-9), pages 1356-1373, June.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:8-9:p:1356-1373
    DOI: 10.1002/mana.201600083
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    Cited by:

    1. Jun O'Hara & Gil Solanes, 2020. "Erratum to the paper “Regularized Riesz energies of submanifolds”: (Published in Math. Nachr. 291 (2018), no. 8–9, 1356–1373)," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 1014-1019, May.
    2. Jun O'Hara, 2023. "Self‐repulsiveness of energies for closed submanifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 296(2), pages 797-810, February.

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