TY - JOUR
T1 - Regularized Riesz energies of submanifolds
AU - O'Hara, Jun
AU - Solanes, Gil
PY - 2018/6/1
Y1 - 2018/6/1
N2 - © 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.
AB - © 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.
KW - Hadamard regularization
KW - Riesz potential
KW - analytic continuation
KW - energy
KW - fractional perimeter
UR - https://www.scopus.com/pages/publications/85043346783
U2 - 10.1002/mana.201600083
DO - 10.1002/mana.201600083
M3 - Article
SN - 0025-584X
VL - 291
SP - 1356
EP - 1373
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 8-9
ER -