The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$

Yilin Wang

doi:10.4171/jems/876

JournalsjemsVol. 21, No. 7pp. 1915–1941

The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE $_{0 +}$

Yilin Wang
ETH Zürich, Switzerland

$The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$ cover$

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Abstract

We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function. In particular, using an interpretation of this energy as a large deviation rate function for SLE $_{κ}$ as $κ \to 0$ and the known reversibility of the SLE $_{κ}$ curves for small $κ$ , we show that the energy of a deterministic curve from one boundary point $a$ of a simply connected domain $D$ to another boundary point $b$ is equal to the energy of its time-reversal, ie. of the same curve but viewed as going from $b$ to $a$ in $D$ .

Cite this article

Yilin Wang, The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE $_{0 +}$ . J. Eur. Math. Soc. 21 (2019), no. 7, pp. 1915–1941

DOI 10.4171/JEMS/876