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

In the paper we prove that, for $\kappa \in (0,8)$, the $n$-point boundary Green’s function of exponent $\frac{8}{\kappa }-1$ for chordal SLE${}_{\kappa }$ 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.