EVENT DETAILS AND ABSTRACT

Title: Boundary Green's Function and Minkowski Content of SLE_\kappa(\rho)
Speaker: Dapeng Zhan
Speaker Info: Michigan State University
Brief Description:
Special Note:
Abstract:

We prove the existence 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 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.