A Möbius invariant discretization of O’Hara’s Möbius energy-Reference-Cited by-同舟云学术

A Möbius invariant discretization of O’Hara’s Möbius energy

Published:2022-03 Issue:03 Volume:31 Page:
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Blatt Simon¹^ORCID,Ishizeki Aya²,Nagasawa Takeyuki²

Affiliation:

1. Departement of Mathematics, Paris Lodron Universität Salzburg, Hellbrunner Strasse 34, 5020 Salzburg, Austria

2. Departement of Mathematics, Graduate School of Science and Engineering, Saitama University, Saitama 338-8570, Japan

Abstract

We introduce a new discretization of O’Hara’s Möbius energy. In contrast to the known discretizations of Simon and Kim and Kusner it is invariant under Möbius transformations of the surrounding space. The starting point for this new discretization is the cosine formula of Doyle and Schramm. We then show [Formula: see text]-convergence of our discretized energies to the Möbius energy.

Funder

Austrian Science Fund

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021821652250016X

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