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1403 Circle Drive, Knoxville, TN 37996

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SPEAKER: Jared Krandel (Stony Brook University)

TITLE: Uniformly rectifiable metric spaces satisfy the weak constant density condition.

ABSTRACT: The weak constant density condition (WCD) is a quantitative regularity property introduced by David and Semmes in their foundational work on uniformly rectifiable subsets of Euclidean space. Roughly speaking, a space satisfies the WCD if in \textit{most} balls, the space supports a measure with \textit{nearly constant} density in a neighborhood of scales and locations. In this talk, we discuss the ideas behind a proof that uniformly rectifiable \textit{metric spaces} satisfy the WCD. This theorem gives a metric space analog of a Euclidean result of David and Semmes.

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