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math.CA2025
Quantitative differentiability on uniformly rectifiable sets
Jonas Azzam, Mihalis Mourgoglou, Michele Villa
We prove quantitative differentiability estimates for functions defined on uniformly rectifiable subsets of the Euclidean space. More precisely, we show that a Dorronsoro-typ…
math.CA2024
Analytic capacity and dimension of sets with plenty of big projections
Damian DÄ browski, Michele Villa
Our main result marks progress on an old conjecture of Vitushkin. We show that a compact set in the plane with plenty of big projections (PBP) has positive analytic capacity, along…