54 citations · 168 across the 18 of their papers we have counts for
12 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 kno…
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…
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…
Circle homeomorphisms with square summable diamond shears
Dragomir Šarić, Yilin Wang, Catherine Wolfram
We introduce and the study the space of homeomorphisms of the circle (up to Möbius transformations) which are in with respect to modular coordinates called diamond shears…
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 .…
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…
Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines
Fredrik Viklund, Yilin Wang
The Loewner energy of a Jordan curve is the Dirichlet energy of its Loewner driving term. It is finite if and only if the curve is a Weil-Petersson quasicircle. In this paper, we d…
A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops
Yilin Wang
In this note, we establish an expression of the Loewner energy of a Jordan curve on the Riemann sphere in terms of Werner's measure on simple loops of SLE type. The proof i…
Equivalent Descriptions of the Loewner Energy
Yilin Wang
Loewner's equation provides a way to encode a simply connected domain or equivalently its uniformizing conformal map via a real-valued driving function of its boundary. The first m…
Remarks on Loewner Chains Driven by Finite Variation Functions
Atul Shekhar, Huy Tran, Yilin Wang
To explore the relation between properties of Loewner chains and properties of their driving functions, we study Loewner chains driven by functions of finite total variation. U…
The Loewner energy of loops and regularity of driving functions
Steffen Rohde, Yilin Wang
Loewner driving functions encode simple curves in 2-dimensional simply connected domains by real-valued functions. We prove that the Loewner driving function of a curve (…
The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE
Yilin Wang
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 interpretat…