Green's function for cut points of chordal SLE attached with boundary arcs
Dapeng Zhan · arXiv (Cornell University) · 2020
Let $κ\in(4,8)$. Let $γ$ be an SLE$_κ$ curve in a Jordan domain $D$ connecting $a_1 e a_2\in\partial D$. We attach $γ$ with two open boundary arcs $A_1,A_2$ of $D$, which share end points $b_1 e b_2\in\partial D\setminus\{a_1,a_2\}$, and consider for each $z_0\in D$ the limit $$ \lim_{r \downarrow 0}r^{1-\frac 38κ} \mathbb{P}[γ\cup A_1\cup A_2 \mbox{ has a cut point in }\{|z-z_0|