Department of Mathematics


  •  Dapeng Zhan, MSU
  •  Boundary Green's function and Minkowski content for SLE$_\kappa(\rho)$
  •  10/26/2022
  •  3:00 PM - 3:50 PM
  •  C405 Wells Hall
  •  Dapeng Zhan (

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.



Department of Mathematics
Michigan State University
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