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

## TL;DR

This paper investigates the behavior of solutions to the chordal Komatu-Loewner equation near explosion time, revealing convergence properties and extending results to stochastic evolutions, thus deepening understanding of slit dynamics in complex analysis.

## Contribution

It provides new insights into the asymptotic behavior of solutions near explosion time and extends these results to stochastic Komatu-Loewner evolutions.

## Key findings

- Distance between slits and driving function converges to zero at explosion time
- Asymptotic behavior holds for stochastic evolutions under natural assumptions
- Enhances understanding of slit dynamics in the upper half-plane

## Abstract

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 (2008) and by Chen and Fukushima (2018). The solution to this equation represents moving slits in the upper half-plane. We show that the distance between the slits and driving function converges to zero at its explosion time. We also prove a probabilistic version of this asymptotic behavior for stochastic Komatu-Loewner evolutions under some natural assumptions.