Prof. Mitsuhiro Shishikura, gave a lecture titled “Oscillating wandering domain for a transcendental entire function of class B” at AMSS on 16, May 2018.
C. Bishop has introduced a technique called quasiconformal folding, and as an application, constructed a transcendental entire function of class B (with bounded singular values) having an oscillating wandering domain. However, there are several issues in the proof. In this talk, they proposed a new construction which used quasiconformal mappings but not Bishop's quasiconformal folding. With their method they can show that the obtained function had finite order. They used an estimate on the variation of cross-ratio under quasiconformal mappings, which led to a new proof of Teichmueller-Wittich-Belinskii’s theorem on the conformality at a point. This was a joint work with David Marti Pete.

Prof. Mitsuhiro Shishikura is from Kyoto University.