P. Mattila

activity

20082023

most citedAhlfors-David regular sets and bilipschitz maps

52 citations · 92 across the 13 of their papers we have counts for

collaborators

17 papers

math.CA2023

Hausdorff dimension of plane sections and general intersections

Pertti Mattila

This paper extends some results of [M5] and [M3], in particular, removing assumptions of positive lower density. We give conditions on a general family $P_λ:\mathbb{R}^{n}\to\mathb…

math.CA2023

A survey on the Hausdorff dimension of intersections

Pertti Mattila

Let $A$ and $B$ be Borel subsets of the Euclidean $n$ -space with $dim A + dim B > n$ . This is a survey on the question: what can we say about the Hausdorff dimension of the inter…

math.CA2021

Rectifiability; a survey

Pertti Mattila

This is a survey on rectifiability. I discuss basic properties of rectifiable sets, measures, currents and varifolds and their role in complex and harmonic analysis, potential theo…

math.CA2021

Parabolic rectifiability, tangent planes and tangent measures

Pertti Mattila

We define rectifiability in $R^{n} \times R$ with a parabolic metric in terms of $C^{1}$ graphs and Lipschitz graphs with small Lipschitz constants and we characteriz…

math.CA2020

Hausdorff dimension of intersections with planes and general sets

Pertti Mattila

We give conditions on a general family $P_{λ} : R^{n} \to R^{m}, λ \in Λ,$ of orthogonal projections which guarantee that the Hausdorff dimension formula $dim A \cap P_{λ}^{- 1} {u} = s - m$ hold…

math.CA2020

Hausdorff dimension and projections related to intersections

Pertti Mattila

For $S_{g} (x, y) = x - g (y), x, y \in R^{n}, g \in O (n),$ we investigate the Lebesgue measure and Hausdorff dimension of $S_{g} (A)$ given the dimension of $A$ , both for general Borel sub…