Jun 11, 2019
Interplay between the Loewner and Dirichlet energies: Conformal welding and Flow-lines
Date: June 11, 2019 |
5:30 pm –
6:30 pm
Speaker:
Yilin Wang, ETH Zürich
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
In this talk we present 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 deduce also an identity on complex valued fields that combines both welding and flow-line identities. 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.