Ikkei Hotta

Chordal Loewner chains with quasiconformal extensions

In 1972, Becker (J Reine Angew Math 255:23–43, 1972), discovered a construction of quasiconformal extensions making use of the classical radial Loewner chains. In this paper we develop a chordal analogue of Becker’s construction. As an application, we establish new sufficient conditions for quasiconformal extendibility of holomorphic functions and give a simplified proof of one well-known result by Becker and Pommerenke (J Reine Angew Math 354:74–94, 1984) for functions in the half-plane.

Tightness Results for Infinite-Slit Limits of the Chordal Loewner Equation

In this note, we consider a multi-slit Loewner equation with constant coefficients that describes the growth of multiple SLE curves connecting N points on

\Phi

\mathbb {R}

Hydrodynamic Limit of Multiple SLE

R to infinity within the upper half-plane. For every

Explicit quasiconformal extensions and Löwner chains

N\in \mathbb {N}

Boundedness, univalence and quasiconformal extension of Robertson functions

N∈N, this equation yields a measure-valued process