Pertti Mattila

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20232026

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math.CA2026

On the parabolic Hausdorff dimension of orthogonal projections

Terence L. J. Harris, Pertti Mattila

For Borel sets $A \subset R^{n} \times R$ we prove lower bounds for the parabolic Hausdorff dimension of the orthogonal projections of $A$ on generic $m$ -dimensional…

math.CA2024

Packing sets in Euclidean space by affine transformations

Alex Iosevich, Pertti Mattila, Eyvindur Palsson +4

For Borel subsets $Θ \subset O (d) \times R^{d}$ (the set of all rigid motions) and $E \subset R^{d}$ , we define \begin{align*} Θ(E):=\bigcup_{(g,z)\in Θ}(gE+z). \end{ali…

math.CA2023

Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension

J. Cufí, J. J. Donaire, P. Mattila +1

Consider a standard Cantor set in the plane of Hausdorff dimension 1. If the linear density of the associated measure $μ$ vanishes, then the set of points where the principal value…