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

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.