The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE0+_{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 SLEκ_{\kappa} as κ0\kappa \to 0 and the known reversibility of the SLEκ_{\kappa} curves for small κ\kappa, we show that the energy of a deterministic curve from one boundary point aa of a simply connected domain DD to another boundary point bb is equal to the energy of its time-reversal, ie. of the same curve but viewed as going from bb to aa in DD.

Cite this article

Yilin Wang, The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE0+_{0+}. J. Eur. Math. Soc. 21 (2019), no. 7, pp. 1915–1941

DOI 10.4171/JEMS/876