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 2021Show all

3 papers · 1 filter

math.CA2021

A note on the Hausdorff dimension of uniformly non flat sets with plenty of big projections

Michele Villa

Using a recent result of Orponen (Invent. math. '21), we show that sets with plenty of big projections (PBP) admit an Analyst's Travelling Salesman Theorem. We then show that sets…

math.CA2021

Integrability of orthogonal projections, and applications to Furstenberg sets

Damian Dąbrowski, Tuomas Orponen, Michele Villa

Let $G (d, n)$ be the Grassmannian manifold of $n$ -dimensional subspaces of $R^{d}$ , and let $π_{V} : R^{d} \to V$ be the orthogonal projection. We p…

math.CA2021★ 1 cited

Cone and paraboloid points of arbitrary subsets of Euclidean space

Matthew Hyde, Michele Villa

In this paper we characterise cone points of arbitrary subsets of Euclidean space. Given $E \subset R^{n}$ , $x \in E$ is a cone point of $E$ if and only if \begin{align*} \i…