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A deterministic proof of Loewner energy reversibility via local reversals
Jinwoo Sung · 2024-08-01 · via math.PR updates on arXiv.org

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 Yilin Wang (arXiv:1601.05297) 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$_κ$ as $κ\to 0$. Our method is similar in spirit to Dapeng Zhan's proof (arXiv:0808.3649) of chordal SLE$_κ$ reversibility for $κ\in (0,4]$, though it is purely deterministic. As a key step in our proof, we establish that a minimimal energy chord among those passing through a fixed finite set of points is a piecewise hyperbolic geodesic.

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