Horizontal Besicovitch sets of measure zero and some related problems

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Analysis Seminar

Thursday, November 16, 2023 - 3:30pm

Terence Harris

University of Wisconsin-Madison

Location

University of Pennsylvania

DRL 3C2

We show that horizontal Besicovitch sets of measure zero exist in R^3. The proof is constructive and uses point-line duality analogously to Kahane’s construction of measure zero Besicovitch sets in the plane. Some consequences and related examples are discussed for the SL_2 Kakeya maximal function.

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