S. Gardiner

will speak on

Boundary points of angular type form a set of zero harmonic measure

Time: 3:00PM
Date: Tue 11th October 2022
Location: Seminar Room SCN 1.25 [map]

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Abstract: A boundary point w of a planar domain W is called 'angular' if there exists $r > 0$ such that each component of the set $\{z \in W: |z-w| < r\}$ which has $w$ as a boundary point is contained in an angle of vertex w and aperture less than $\pi$. This talk will provide answers to the following problems that were submitted by Dvoretzky in 1974 to Hayman's collection of 'Research problems in function theory':
1) Prove, by non-probabilistic methods, that the set of angular boundary points of a planar domain has zero harmonic measure.
2) Does the same conclusion hold when angles less than $\pi$ are replaced by more general approach regions?
3) Is there a corresponding result in higher dimensions?

(Joint work with Tomas Sjodin)

(This talk is part of the Analysis series.)

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