Existence of multi-point boundary Green’s function for chordal Schramm-Loewner evolution (SLE)

Abstract

In the paper we prove that, for $\mathrm{\kappa }\in (0,8)$, the n-point boundary Green’s function of exponent $\frac{8}{\mathrm{\kappa }}-1$ for chordal SLE${}_{\mathrm{\kappa }}$ exists. We also prove that the convergence is uniform over compact sets and the Green’s function is continuous. We also give up-to-constant bounds for the Green’s function.