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 as and the known reversibility of the SLE curves for small , we show that the energy of a deterministic curve from one boundary point of a simply connected domain to another boundary point is equal to the energy of its time-reversal, ie. of the same curve but viewed as going from to in .
Cite this article
Yilin Wang, The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE. J. Eur. Math. Soc. 21 (2019), no. 7, pp. 1915–1941DOI 10.4171/JEMS/876