• Speaker: Dapeng Zhan, MSU
• Title: Boundary Green's function and Minkowski content for SLE$_\kappa(\rho)$
• Date: 10/26/2022
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall
• Contact: Dapeng Zhan (zhan@msu.edu)

We prove the existence of the Minkowski content of the intersection of an SLE$_\kappa(\rho)$ curve with a real interval using the standard approach, which is to estimate the convergence rate of one-point and two-point boundary Green's functions of SLE$_\kappa(\rho)$. Then we show the existence of a conformally covariant measure called Minkowski content measure on the intersection of an SLE$_\kappa(\rho)$ curve with a half real line, which is closely related to the Minkowski content. Using the Minkowski content measure, we construct rooted and unrooted SLE$_\kappa(\rho)$ bubble measures, which are supported on loops and satisfy SLE$_\kappa(\rho)$-type domain Markov property.