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arXiv · 1803.00194

Chordal Komatu-Loewner equation for a family of continuously growing hulls

Takuya Murayama
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Abstract

In this paper, we discuss the chordal Komatu-Loewner equation on standard slit domains in a manner applicable not just to a simple curve but also a family of continuously growing hulls. Especially a conformally invariant characterization of the Komatu-Loewner evolution is obtained. As an application, we prove a sort of conformal invariance, or locality, of the stochastic Komatu-Loewner evolution $\mathrm{SKLE}_{\sqrt{6}, -b_{\mathrm{BMD}}}$ in a fully general setting, which solves an open problem posed by Chen, Fukushima and Suzuki [Stochastic Komatu-Loewner evolutions and SLEs, Stoch. Proc. Appl. 127 (2017), 2068-2087].

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Takuya Murayama. 2018-09-04. Chordal Komatu-Loewner equation for a family of continuously growing hulls. https://doi.org/10.1016/j.spa.2018.08.012

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