Multiple-paths $SL{E}_{\kappa }$ in multiply connected domains

Abstract

We define multiple-paths Schramm-Loewner evolution ($SL{E}_{\kappa }$) in multiply connected domains when $\kappa \le 4$ and prove that in annuli, the partition function is smooth. Moreover, we give up-to-constant estimates for the partition function of bi-chordal annulus $SL{E}_{\kappa }$ measure and we establish a connection between this measure and two-sided $SL{E}_{\kappa }$ in the unit disk.