Title: Harmonic measure and Geometric Measure Theory: no regularity two phase fee boundary problem

Date: 10/17/2016

Time: 4:02 PM - 4:52 PM

Place: C517 Wells Hall

Harmonic measure and Geometric Measure Theory: no regularity two phase fee boundary problem
We will show how from absolute continuity of outer and inner harmonic measures one can deduce the rectifiability of the common boundary.
This solves the problem of Bishop from the early 90's.
This requires the combination of the technique from the GMT and the new technique of non-homogeneous harmonic analysis
elaborated by Nazarov-Treil-Volberg and Tolsa and his school.
This is a joint work with J. Azzam, M. Mourgoglou and X. Tolsa.