Abstract
It was shown in a preceding paper that the Möbius energy can be decomposed into three parts and the Möbius invariance of each part was investigated. In this paper, we provide analytic application of our decomposition. Variational formulae of the Möbius 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.
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Acknowledgments
The authors would like to express their gratitude to Professor O’Hara for discussions on their results.
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T. Nagasawa is partly supported by Grant-in-Aid for scientific Research (C) (No. 25400156), Japan Society for the Promotion of Science.
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Ishizeki, A., Nagasawa, T. A decomposition theorem of the Möbius energy II: variational formulae and estimates. Math. Ann. 363, 617–635 (2015). https://doi.org/10.1007/s00208-015-1175-2
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DOI: https://doi.org/10.1007/s00208-015-1175-2