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arXiv · 1601.05297

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

Yilin Wang
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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 $κ$ tends 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.

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Yilin Wang. 2019-03-08. The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$. https://doi.org/10.4171/jems%2F876

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