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.