Time-reversal of multiple-force-point SLE$_\kappa(\underline\rho)$ with all force points lying on the same side

TL;DR

This paper introduces new intermediate and reversed SLE processes using hypergeometric functions to describe the time-reversal of multiple-force-point SLE curves with all force points on the same boundary side under specific parameter conditions.

Contribution

It defines novel intermediate and reversed SLE processes with hypergeometric functions and characterizes the time-reversal of multiple-force-point SLE curves in boundary configurations.

Findings

Defined intermediate and reversed SLE processes using hypergeometric functions.

Characterized the time-reversal of multiple-force-point SLE curves with all force points on the same boundary side.

Established conditions on ppa and ar ho for the results to hold.

Abstract

We define intermediate SLE$_\kappa(\underline\rho)$ and reversed intermediate SLE$_\kappa(\underline\rho)$ processes using Appell-Lauricella multiple hypergeometric functions, and use them to describe the time-reversal of multiple-force-point chordal SLE$_\kappa(\underline\rho)$ curves in the case that all force points are on the boundary and lie on the same side of the initial point, and $\kappa $ and $\underline\rho=(\rho_1,\dots,\rho_m)$ satisfy that either $\kappa\in(0,4]$ and $\sum_{j=1}^k \rho_j>-2$ for all $1\le k\le m$, or $\kappa\in(4,8)$ and $\sum_{j=1}^k \rho_j\ge \frac{\kappa}{2}-2$ for all $1\le k\le m$.