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Quantitative control of the epsilon-function determines regularity

Emily Casey, University of Washington
Thursday, May 9, 2024 - 12:30pm to 1:20pm
PDL C-401

A longstanding conjecture of Carleson stated that the tangent points of the boundaries of certain planar domains can be characterized by the behavior of the Carleson \varepsilon-function. This conjecture, which was fully resolved by Jaye, Tolsa, and Villa in 2021, established that having some Dini type control of the Carleson \varepsilon-function implied the existence of tangents. A natural question is whether quantitative control on this function implies better regularity results. In this talk, we will present results that give a positive answer to this question. This is ongoing work. 

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