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

Simon Blatt; Aya Ishizeki; Takeyuki Nagasawa

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

Simon Blatt^*, Aya Ishizeki, Takeyuki Nagasawa

^*Corresponding author for this work

Mathematics

Research output: Working paper/Preprint › Preprint

Abstract

We introduce a new discretization of O'Hara's M\"obius energy. In contrast to the known discretizations of Simon and Kim and Kusner it is invariant under M\"obius transformations of the surrounding space. The starting point for this new discretization is the cosine formula of Doyle and Schramm. We then show $\Gamma$-convergence of our discretized energies to the M\"obius energy under very natural assumptions.

Original language	English
Publication status	Published - 21 Sept 2018

Publication series

Name	arXiv

Keywords

math.FA
math.GT
math.NA
57M25, 49Q10, 53A04

Fields of Science and Technology Classification 2012

101 Mathematics

Cite this

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abstract = " We introduce a new discretization of O'Hara's M\{"}obius energy. In contrast to the known discretizations of Simon and Kim and Kusner it is invariant under M\{"}obius transformations of the surrounding space. The starting point for this new discretization is the cosine formula of Doyle and Schramm. We then show $\Gamma$-convergence of our discretized energies to the M\{"}obius energy under very natural assumptions. ",

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AU - Blatt, Simon

AU - Ishizeki, Aya

AU - Nagasawa, Takeyuki

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Y1 - 2018/9/21

N2 - We introduce a new discretization of O'Hara's M\"obius energy. In contrast to the known discretizations of Simon and Kim and Kusner it is invariant under M\"obius transformations of the surrounding space. The starting point for this new discretization is the cosine formula of Doyle and Schramm. We then show $\Gamma$-convergence of our discretized energies to the M\"obius energy under very natural assumptions.

AB - We introduce a new discretization of O'Hara's M\"obius energy. In contrast to the known discretizations of Simon and Kim and Kusner it is invariant under M\"obius transformations of the surrounding space. The starting point for this new discretization is the cosine formula of Doyle and Schramm. We then show $\Gamma$-convergence of our discretized energies to the M\"obius energy under very natural assumptions.

KW - math.FA

KW - math.GT

KW - math.NA

KW - 57M25, 49Q10, 53A04

M3 - Preprint

T3 - arXiv

BT - A Möbius invariant discretization of O'Hara's Möbius energy

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