For the last two decades, the Loewner equation, which describes the time-evolution of conformal mappings on simply connected domains, has paid attention in relation to Schramm-Loewner evolution (SLE). Now, there are many SLE-like stochastic objects such as multiple-paths SLE. For their generalization towards multiply connected domains, some people have worked on the Komatu-Loewner equation lately. However, even in the case where the corresponding hull is multiple paths, the known results are not enough to construct multiple-paths "SKLE". In this talk, we establish the chordal Komatu-Loewner equation, making use of the complex Poisson kernel of Brownian motion with darning (BMD), for a wide range of hulls generally not driven by point driving sources.

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# Loewner chains and evolution families on parallel slit half-planes

Takuya Murayama, Kyoto University, Japan

Monday, October 14, 2019 - 2:30pm to 3:20pm

LOW 101