Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions
Carlos E. Kenig, David Preiss, Tatiana Toro · Journal of the American Mathematical Society · 2008
In this work we introduce the use of powerful tools from geometric measure theory (GMT) to study problems related to the size and structure of sets of mutual absolute continuity for the harmonic measure ω + \omega ^+ of a domain Ω = Ω + ⊂ R n \Omega =\Omega ^+\subset \mathbb {R}^n and the harmonic measure ω − \omega ^- of Ω − \Omega ^- , Ω − = int ( Ω c ) \Omega ^-=\mbox {int}(\Omega ^c) , in dimension n ≥ 3 n\ge 3 .