Research
See my arXiv preprints. Here’s my ResearchGate page.
Preprints
with I. Fleschler and X. Tolsa. The Alt-Caffarelli-Friedman monotonicity formula and Carleson’s $\varepsilon^2$-conjecture in higher dimensions. ArXiv preprint, 2023.
with J. Azzam and M. Mourgoglou. Quantitative differentiation on uniformly rectifiable sets. ArXiv preprint, 2023.
Published articles
- Carleson’s $\varepsilon^2$-conjecture in higher dimensions.
with I. Fleschler and X. Tolsa. Accepted by Invent. Math.
arXiv
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- Ricci curvature bounded below and uniform rectifiability.
with M. Hyde and I.Y. Violo. Published in Ann. Fenn. Math.
arXiv | article
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- Analytic capacity of sets with plenty of big projections and Vitushkin conjecture.
with D. Dąbrowski. Published in Trans. Amer. Math. Soc.
arXiv | article
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- Structure of sets with nearly maximal Favard length
with A. Chang, D. Dąbrowski and T. Orponen. Analysis & PDEs.
arXiv | article
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- Integrability of orthogonal projections, and applications to Furstenberg sets
with D. Dąbrowski and T. Orponen. Adv. Math.
arXiv | article
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- Sub-elliptic boundary value problems in flag domains
with T. Orponen. Adv. Calc. Var.
article
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- Necessary condition for the $L^2$ boundedness of the Riesz transform in Heisenberg groups
with D. Dąbrowski. Math. Proc. Cam. Phil. Soc.
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- A square function involving the center of mass and rectifiability.
Math. Zeitschrift.
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- A proof of Carleson $\varepsilon^2$-conjecture.
with B. Jaye and X. Tolsa. Ann. of Math.
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- $Ω$-symmetric measures and related singural integrals.
Rev. Mat. Iberoam.
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- Quantitative comparisons of multiscale geometric properties.
with J. Azzam. Analysis & PDEs.
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- Tangent points of $d$-lower content regular sets and $\beta$ numbers.
J. Lond. Math. Soc.
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Old preprints and notes
Villa M. A note on Hausdorff dimension of sets with plenty of big projection. ArXiv preprint (2021).
with M. Hyde. Cone and paraboloid points of arbitrary subsets of Euclidean space. ArXiv preprint (2021).
Higher dimensional Jordan curves. Arxiv preprint (2019).