A decomposition theorem of the Möbius energy I: Decomposition and Möbius invariance

Abstract

The Möbius energy, defined for closed curves embedded in Rⁿ, is decomposed into three parts. It is called the Möbius energy since it is invariant under Möbius transformations. An alternative proof of the Möbius invariance is given using the decomposition. Furthermore the invariance of each part of decomposition is discussed.