Regularized Riesz energies of submanifolds

Jun O'Hara, Gil Solanes

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)


© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 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.
Original languageEnglish
Pages (from-to)1356-1373
JournalMathematische Nachrichten
Issue number8-9
Publication statusPublished - 1 Jun 2018


  • Hadamard regularization
  • Riesz potential
  • analytic continuation
  • energy
  • fractional perimeter


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