Year: 2025
Type: article
Abstract: We give a new proof of the orientation reversibility of chordal Loewner energy by reversing the orientation of a chord in partial increments. This fact was first proved by Wang (2019) using the reversibility of chordal Schramm–Loewner evolution (SLE) along with the interpretation of Loewner energy as the large deviation rate function of chordal SLE\(_\kappa\) as \(\kappa \to 0\). Our method is similar in spirit to Zhan's proof (2008) of chordal SLE\(_\kappa\) reversibility for \(\kappa \in (0,4]\), though it is purely deterministic. As a key step in our proof, we establish that a minimal energy chord among those passing through a fixed finite set of points is a piecewise hyperbolic geodesic.
Source: Annales Fennici Mathematici
DOI: 10.54330/afm.163173
Author: Jinwoo Sung
Institution: University of Chicago
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411795987