Seminar Event Detail

Complex Analysis, Dynamics and Geometry

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 non-removable for quasiconformal maps and thus for W^{1,p} functions, for 1 leq p leq 2. The argument involves the construction of a non-Euclidean sphere, and then the use of the Bonk-Kleiner theorem to embed it quasisymmetrically to the plane.


Speaker:  Dimitrios Ntalampekos
Institution:  UCLA

Event Organizer:     


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