分野別セミナー

The Loewner equation is an evolution equation on the one-parameter family of conformal maps induced from hulls on the upper half-plane. Its generalization to slit domains in the upper half-plane is called the Komatu-Loewner equation. In this case, the ranges of the conformal maps are identified with the moving slits whose dynamics are determined by the Komatu-Loewner equation for the slits. In this talk, I shall provide a systematic treatment of these equations under a general assumption on the continuity of hulls. If time permits, I shall also explain the following results that are derived from our treatment:
*Locality of stochastic Komatu-Loewner evolution
*Characterization of the explosion time of the evolution