Quasiconformal mappings are generalizations of conformal mappings. There are 3 main definitions of quasiconformality: metric, geometric and analytic one. Their equivalence is known in various metric measure space settings. However, until recent work by Ackermann (2010) and Gartland, Jung, and Romney (2016), modern theory was unable to cover the case of the Grushin plane. The talk will start with basic definitions of quasiconformality in Euclidean spaces and example of the appearance of quasiregular mapping in Physics. We will proceed with defining quasiconformal mappings in a more general sense, outline general knowledge about the equivalence of definitions in metric measure spaces, and finally, provide recent development of this theory on the Grushin plane.
Meeting ID: 828 4242 2342 Passcode: 274475