Chordal KomatuLoewner equation for a family of continuously growing hulls
Abstract
In this paper, we discuss the chordal KomatuLoewner 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 KomatuLoewner evolution is obtained. As an application, we prove a sort of conformal invariance, or locality, of the stochastic KomatuLoewner 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 KomatuLoewner evolutions and SLEs, Stoch. Proc. Appl. 127 (2017), 20682087].
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1803.00194
 Bibcode:
 2018arXiv180300194M
 Keywords:

 Mathematics  Probability;
 Mathematics  Complex Variables;
 60J67 (Primary) 30C20;
 60J70;
 60H10 (Secondary)
 EPrint:
 The results on the explosion of KomatuLoewner evolutions contained in the first version will appear in another paper