4 papers
Univalence and holomorphic extension of the solution to -controlled Loewner-Kufarev equations
Takafumi Amaba, Roland Friedrich, Takuya Murayama
We prove that a solution to the -controlled Loewner-Kufarev equation, which was introduced by the first two authors, exists uniquely, is univalent and starlike on the unit disk…
Reformulation of Laplacian- motion in terms of stochastic Komatu-Loewner evolution in the chordal case
Takuya Murayama
We investigate the relation between the Laplacian- motion and stochastic Komatu-Loewner evolution (SKLE) on multiply connected subdomains of the upper half-plane, both of which…
On the slit motion obeying chordal Komatu-Loewner equation with finite explosion time
Takuya Murayama
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 (20…
Chordal Komatu-Loewner equation for a family of continuously growing hulls
Takuya Murayama
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 h…