Energy of embedded surfaces invariant under Moebius tranformations, addendum

TL;DR

This paper discusses a Moebius-invariant energy for embedded surfaces, highlighting its properties and a compactness result for a variant, with detailed proofs to be published later.

Contribution

It introduces a new Moebius-invariant energy for surfaces and proves a compactness property for a variant of this energy.

Findings

The energy is invariant under Moebius transformations.

The round sphere uniquely minimizes the energy.

A compactness property for a variant of the energy is established.

Abstract

In a previous preprint we defined an energy associated to every embedding of a surface into $R^n$ or $S^n$. This energy is invariant under Moebius tranformations and the "round" sphere is its only absolute minimum. Here we sketch a proof of the compactness property for a variant of it. The details will appear elsewhere.