The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE0+

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 as κ tends to 0 and the known reversibility of the SLEκ 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 (© Cornell University 2020).