A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops

Abstract

In this note, we establish an expression of the Loewner energy of a Jordan curve on the Riemann sphere in terms of Werner's measure on simple loops of SLE${}_{8/3}$ type. The proof is based on a formula for the change of the Loewner energy under a conformal map that is reminiscent of the restriction properties derived for SLE processes.

11 pages, 3 figures

References in corpus (2)

• Equivalent Descriptions of the Loewner Energy
• The Loewner energy of loops and regularity of driving functions

Cited by in corpus (2)

• The Loewner-Kufarev Energy and Foliations by Weil-Petersson Quasicircles
• Weil-Petersson Teichmüller space III: dependence of Riemann mappings for Weil-Petersson curves