Michele Villa

activity

20172023

most citedQuantitative Comparisons of Multiscale Geometric Properties

8 citations · 23 across the 13 of their papers we have counts for

collaborators

Showing 2019Show all

5 papers · 1 filter

math.CA2019

A proof of Carleson's $ε^{2}$ -conjecture

Benjamin Jaye, Xavier Tolsa, Michele Villa

In this paper we provide a proof of the Carleson $ε^{2}$ -conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of…

math.CA2019★ 1 cited

A square function involving the center of mass and rectifiability

Michele Villa

For a Radon measure $μ$ on $R^{d}$ , define $C_{μ}^{n} (x, t) = (\frac{1}{t ^{n}} ∣ \int_{B (x, t)} \frac{x - y}{t} d μ (y) ∣)$ . This coefficient quantifies how symmetric the meas…

math.CA2019★ 7 cited

Higher dimensional Jordan curves

Michele Villa

We address the question of what is the correct higher dimensional analogue of Jordan curves from the point of view of quantitative rectifiability. More precisely, we show that 'top…

math.CA2019

$Ω$ -symmetric measures and related singular integrals

Michele Villa

Let $S \subset C$ be the circle in the plane, and let $Ω : S \to S$ be an odd bi-Lipschitz map with constant $1 + δ_{Ω}$ , where $δ_{Ω} > 0$ is small. Ass…

math.AP2019★ 8 cited

Quantitative Comparisons of Multiscale Geometric Properties

Jonas Azzam, Michele Villa

We generalize some characterizations of uniformly rectifiable (UR) sets to sets whose Hausdorff content is lower regular (and in particular, do not need to be Ahlfors regular). For…

A proof of Carleson's ε2-conjecture

A square function involving the center of mass and rectifiability

Higher dimensional Jordan curves

Ω-symmetric measures and related singular integrals

Quantitative Comparisons of Multiscale Geometric Properties

A proof of Carleson's $ε^{2}$ -conjecture

$Ω$ -symmetric measures and related singular integrals