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The Loewner Energy via the Renormalised Energy of Moving Frames

2021/11/29 by Michelat, Alexis, Wang, Yilin
#30C35 #53C42 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.14748

Abstract

We obtain a new formula for the Loewner energy of Jordan curves on the sphere, which is a Kähler potential for the essentially unique Kähler metric on the Weil-Petersson universal Teichmüller space, as the renormalised energy of moving frames on the two domains of the sphere delimited by the given curve.

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