G. Dall’Ara

activity

20242026

collaborators

6 papers

math.MG2026

Rado's covering problem for cubes and balls: a semi-survey

Gian Maria Dall'Ara, Adrian Dumitrescu

What is the largest constant $c \in [0, 1]$ with the property that every finite collection $C$ of axis-parallel squares in the plane admits a disjoint sub-collection $\math…

math.GT2026

Bounded cohomology classes from differential forms

Gian Maria Dall'Ara, Roberto Frigerio, Ervin Hadziosmanovic

Let $M$ be a complete hyperbolic $n$ -manifold, $n \geq 2$ . Via integration over geodesic simplices, any closed bounded differential 2-form on $M$ defines a bounded cohomology class…

math.CA2025

On the best constant in the finitary Vitali covering lemma for high dimensional cubes

Gian Maria Dall'Ara

Let $I^_{d}$ be the largest constant such that every finite collection of cubes in $R^{d}$ whose sides are parallel to the coordinate axes admits a disjoint sub-collection occ…

math.CV2025

The Levi $q$ -core and Property ( $P_{q}$ )

Gian Maria Dall'Ara, Samuele Mongodi, John N. Treuer

We introduce the Grassmannian $q$ -core of a distribution of subspaces of the tangent bundle of a smooth manifold. This is a generalization of the concept of the core previously int…

math.AP2024

On generalized Dirichlet integrals in the smooth and in the o-minimal setting

Gian Maria Dall'Ara

Given a compact manifold $M$ equipped with smooth vector fields $X_{1}, \dots, X_{r}$ , we consider the generalized Dirichlet energy \[\mathbf{E}(f)= \sum_{j=1}^r\int_M |X_jf|^2\, dm,\]…

math.CV2024

Higher dimensional worm domains

Simone Calamai, Gian Maria Dall'Ara

We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codi…