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The Grunsky operator, Ahlfors' question and geometry of Teichmuller spaces


Speaker: Samuel Krushkal, Bar Ilan University
Location: 2112 MSB
Start time: Mon, Feb 28 2011, 4:10PM

We prove the Grinshpan conjecture on the norm of the Grunsky operator generated by univalent functions in the disk. This conjecture is deeply connected with the theory of renormalizations and measurable foliations of dynamical systems, which forces some essential restrictions. The result implies fundamental consequences for the Ahlfors problem concerning quasiconformal extension of holomorphic maps and for geometric, plurisubharmonic and pluripotential features of some Teichmuller spaces.