Date: Monday, February 12, 2018
Location: 3096 East Hall (4:00 PM to 5:00 PM)
Title: (Non)removability of the Sierpinski gasket
Abstract: Removability of sets for quasiconformal maps and Sobolev functions has applications in Complex Dynamics, in Conformal Welding, and in other problems that require "gluing" of functions to obtain a new function of the same class. We, therefore, seek geometric conditions on sets which guarantee their removability. In this talk, I will discuss some very recent results on the (non)removability of the Sierpinski gasket. A first result is that the Sierpinski gasket is removable for continuous functions of the class W^{1,p} for p > 2. The method used applies to more general fractals that resemble the Sierpinski gasket, such as Apollonian gaskets and generalized Sierpinski gasket Julia sets. Then, I will sketch a proof that the Sierpinski gasket is nonremovable for quasiconformal maps and thus for W^{1,p} functions, for 1 leq p leq 2. The argument involves the construction of a nonEuclidean sphere, and then the use of the BonkKleiner theorem to embed it quasisymmetrically to the plane.
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Speaker: Dimitrios Ntalampekos
Institution: UCLA
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