Speaker: Yilin Wang
Title: Coupling theorems for finite energy curves
Abstract:
The Loewner energy defined for Jordan curves is the action functional of
Schramm-Loewner evolution, and is also the SLE's large deviation rate
function with vanishing parameter. We showed recently that a Jordan curve
has finite energy if and only if it is a Weil-Petersson quasicircle, which
is of physics interest providing one of the frameworks for non-perturbative
formulation of string theory. In this talk we present two identities that
relate the Loewner energy to the Dirichlet energy of ambient fields.
They are deterministic analogs of both the welding and flow-line couplings
of SLEs with the Gaussian free field on the level of action functionals.
We apply these results to show that the operation of arclength isometric
welding of two finite energy domains is sub-additive in the energy and that
the energy of equipotentials in a simply connected domain is monotone.
This is a joint work with Fredrik Viklund.