Rectifiability, Interior Approximation and Harmonic Measure

Date: 
Tuesday, February 9, 2016 - 2:00pm
Location: 
Math Sci 111
Speaker: 
Simon Bortz
(MU Math)

 Let D be a domain in R^{n+1} and let K be the set of all points, x, on the boundary of D, for which there exists an open truncated cone with vertex at x that is interior to D. We show that surface measure restricted to K is absolutely continuous with respect to harmonic measure for D. In the plane this is known as McMillan's Theorem. We then show how one can use this to show in a particular setting that surface measure is absolutely continuous with respect to harmonic measure (by showing the cone set, K, has full surface measure). This is joint work with M. Akman, S. Hofmann and J.M. Martell.

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