Multiple-paths $SLE_\kappa$ in multiply connected domains

Abstract

We define multiple-paths Schramm-Loewner evolution ($SLE_\kappa$) in multiply connected domains when $\kappa\leq 4$ 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 $SLE_\kappa$ measure and we establish a connection between this measure and two-sided $SLE_\kappa$ in the unit disk.