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

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 $\Gamma$-convergence of our discretized energies to the Möbius energy under very natural assumptions.