# Chordal Komatu–Loewner equation for a family of continuously growing hulls

@article{Murayama2019ChordalKE, title={Chordal Komatu–Loewner equation for a family of continuously growing hulls}, author={Takuya Murayama}, journal={Stochastic Processes and their Applications}, year={2019} }

Abstract In this paper, we discuss the chordal Komatu–Loewner equation on standard slit domains in a manner applicable not just to a simple curve but also a family of continuously growing hulls. Especially a conformally invariant characterization of the Komatu–Loewner evolution is obtained. As an application, we prove a sort of conformal invariance, or locality, of the stochastic Komatu–Loewner evolution SKLE 6 , − b BMD in a fully general setting, which solves an open problem posed by Chen et…

## 5 Citations

On the slit motion obeying chordal Komatu–Loewner equation with finite explosion time

- MathematicsJournal of Evolution Equations
- 2019

This paper studies the behavior of solutions near the explosion time to the chordal Komatu–Loewner equation for slits, motivated by the preceding studies by Bauer and Friedrich (Math Z 258:241–265,…

Reformulation of Laplacian-$b$ motion in terms of stochastic Komatu-Loewner evolution in the chordal case

- Mathematics
- 2019

We investigate the relation between the Laplacian-$b$ motion and stochastic Komatu-Loewner evolution (SKLE) on multiply connected subdomains of the upper half-plane, both of which are analogues to…

Stochastic Komatu–Loewner Evolutions∗

- 2020

Loewner equation is a differential equation for conformal mappings that can be used to describe evolution of a family of simply connected planar domains. It was introduced by C. Loewner in 1923 in…

On the continuity of half-plane capacity with respect to Carath\'eodory convergence

- Mathematics
- 2021

We study the continuity of half-plane capacity as a function of boundary hulls with respect to the Carathéodory convergence. In particular, our interest lies in the case that hulls are unbounded.…

Loewner chains and evolution families on parallel slit half-planes.

- Mathematics
- 2020

On parallel slit half-planes in the complex plane, we define a Loewner chain as a one-parameter family of univalent functions with expanding images. Then the associated evolution family is defined…

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