Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
We derive the variational formula of the Loewner driving function of a simple chord under infinitesimal quasiconformal deformations with Beltrami coefficients supported away from the chord. As an application, we obtain the first variation of the Loewner energy of a Jordan curve, defined as the Dirichlet energy of its driving …