Explicit expressions for the Loewner energy I^L are obtained as Fredholm determinants of a new operator Λ_φ on the welding homeomorphism, with φ Weil-Petersson precisely when Λ_φ is Hilbert-Schmidt.
Coulomb gas and the Grunsky operator on a Jordan domain with corners.Preprint
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Epstein curves in the hyperbolic disk equate the Schwarzian action to curve length and enclosed area while equaling the derivative of Loewner energy, yielding immediate non-negativity proofs via isoperimetric inequality.
Derives explicit free energy expansion including constant term for determinantal Coulomb gases in quadratic fields with point charge, equating the constant to the Liouville action associated with the droplet.
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On the Loewner energy of a welding homeomorphism
Explicit expressions for the Loewner energy I^L are obtained as Fredholm determinants of a new operator Λ_φ on the welding homeomorphism, with φ Weil-Petersson precisely when Λ_φ is Hilbert-Schmidt.
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Free energy expansion of determinantal Coulomb gases in the quadratic fields with a point charge
Derives explicit free energy expansion including constant term for determinantal Coulomb gases in quadratic fields with point charge, equating the constant to the Liouville action associated with the droplet.