For the last two decades, the Loewner equation, which describes the timeevolution of conformal mappings on simply connected domains, has paid attention in relation to SchrammLoewner evolution (SLE). Now, there are many SLElike stochastic objects such as multiplepaths SLE. For their generalization towards multiply connected domains, some people have worked on the KomatuLoewner equation lately. However, even in the case where the corresponding hull is multiple paths, the known results are not enough to construct multiplepaths "SKLE". In this talk, we establish the chordal KomatuLoewner 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.
Loewner chains and evolution families on parallel slit halfplanes
Takuya Murayama, Kyoto University, Japan

LOW 101