Uniform rectifiability implies $A_{\infty}$-absolute continuity of the harmonic measure with respect to the Hausdorff measure in low dimension.
Joseph Feneuil (Australian National University)
Abstract: Under mild conditions of topology on the domain $\Omega\subset\mathbb R^n$, the harmonic measure is $A_{\infty}$-absolutely continuous with respect to the surface measure if and only if the boundary ∂Ω is uniformly rectifiable of dimension n − 1.
We shall present the state of the art around the above statement, and then discuss the strategy employed by Guy David, Svitlana Mayboroda, and the speaker to extend this characterization of uniform rectifiability to sets of dimension d < n − 1.
analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry
Audience: researchers in the topic
Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.
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| Organizers: | Bruno Poggi*, Ryan Matzke, Jose Luis Luna Garcia* |
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