A M\"obius invariant discretization of O'Hara's M\"obius energy

Simon Blatt; Aya Ishizeki; Takeyuki Nagasawa

A M\"obius invariant discretization of O'Hara's M\"obius energy

Functional Analysis 2018-09-24 v1 Geometric Topology Numerical Analysis

Authors: Simon Blatt , Aya Ishizeki , Takeyuki Nagasawa

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.

Keywords

mobius energy discretization mobius invariance gamma-convergence cosine formula

Cite

@article{arxiv.1809.07984,
  title  = {A M\"obius invariant discretization of O'Hara's M\"obius energy},
  author = {Simon Blatt and Aya Ishizeki and Takeyuki Nagasawa},
  journal= {arXiv preprint arXiv:1809.07984},
  year   = {2018}
}