Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
Sung, Jinwoo; Wang, Yilin
2024

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Abstract

We derive the variational formula of the Loewner driving function of a simple chord under infinitesimal quasiconformal deformations with Beltrami coefficients supported away from the chord. As an application, we obtain the first variation of the Loewner energy of a Jordan curve, defined as the Dirichlet energy of its driving function. This result gives another explanation of the identity between the Loewner energy and the universal Liouville action introduced by Takhtajan and Teo, which has the same variational formula. We also deduce the variation of the total mass of SLE8/3 loops touching the Jordan curve under quasiconformal deformations.

Details

Title
Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
Author
Sung, Jinwoo : University of Chicago : (http://orcid.org/0000-0001-7318-4670)
Wang, Yilin : Institut des Hautes Études Scientifiques
Content Type
Article
Published in
Mathematische Annalen
Identifier(s)
DOI: https://doi.org/10.1007/s00208-024-02866-0
Data availability statement
Data sharing is not applicable to this article as no data sets were generated or analyzed.
Funding Information
Kwanjeong Educational Foundation, Fellowship
European Research Council, RaConTeich, 101116694
Publication Date
2024-04-30
Language
English
Copyright Statement

© The Author(s) 2024

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Physical Sciences Division > Mathematics
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Record Created
2024-10-05

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