A decomposition theorem of the Mobius energy II: variational formulae and estimates

摘要

It was shown in a preceding paper that the Mobius energy can be decomposed into three parts and the Mobius invariance of each part was investigated. In this paper, we provide analytic application of our decomposition. Variational formulae of the Mobius energy have already been obtained by several mathematicians through quite involved calculations. Explicit expressions and estimates of variational formulae can be derived relatively easily by utilizing our decomposition.