5 papers · 1 filter
On the Loewner energy of a welding homeomorphism
Shuo Fan, Fredrik Viklund, Yilin Wang
To any Jordan curve one may associate a circle homeomorphism via conformal welding. Through this correspondence, the Loewner energy , also kn…
Piecewise geodesic Jordan curves II: Loewner energy, projective structures, and accessory parameters
Mario Bonk, Janne Junnila, Steffen Rohde +1
In this paper we consider Jordan curves on the Riemann sphere passing through given points. We show that in each relative isotopy class of such curves, there exists a uni…
Piecewise geodesic Jordan curves I: weldings, explicit computations, and Schwarzian derivatives
Donald Marshall, Steffen Rohde, Yilin Wang
We consider Jordan curves of the form on the Riemann sphere for which each is a hyperbolic geodesic in $(\widehat{\mathbb C} \smallsetminus γ)\cup γ…
Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
Jinwoo Sung, Yilin Wang
We derive the variational formula of the Loewner driving function of a simple chord under infinitesimal quasiconformal deformations with Beltrami coefficients supported away from t…
The Loewner-Kufarev Energy and Foliations by Weil-Petersson Quasicircles
Fredrik Viklund, Yilin Wang
We study foliations by chord-arc Jordan curves of the twice punctured Riemann sphere using the Loewner-Kufarev equation. We associate to such a fol…