Add to ORKGLet $A$ 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 intersections $A\cap (g(B)+z)$ for generic orthogonal transformations $g$ and translations by $z$.Comment: This survey is based on the talk I gave in Karoly Simon's 60+1 birthday conference in Budapest in June 2022. Version 2 improves theorems of Section 6 by removing positive lower density assumtion
We present strong versions of Marstrand's projection theorems and other related theorems. For exampl...
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real li...
We find sets naturally arising in Diophantine approximation whose Cartesian products exceed the expe...
Let A and B be Borel subsets of the Euclidean n-space with dim A + dim B > n and let 0 u for z in a...
Let A and B be Borel subsets of the Euclidean n-space with dim A + dim B > n. This is a survey on th...
For S-g(x, y) = x-g(y), x, y is an element of R-n, g is an element of O(n), we investigate the Lebes...
A classical theorem due to Mattila says that if A, B ⊂ ℝ d of Hausdorff dimension s A , s B respecti...
We give conditions on a general family P-lambda : R-n -> R-m, lambda is an element of Lambda of orth...
I shall discuss some recent developments on two closely related questions: How do projections affect...
l. Introilucti'on. Let m and n be positive integers with m < n and let O*(n, m) be the set o...
The Hausdorff dimension of a product $X\times Y$ can be strictly greater than that of $Y$, even when...
We prove some geometric properties of sets in the first Heisenberg group whose Heisenberg Hausdorff ...
This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets o...
In this paper, we study Hausdorff and Fourier dimension from the point of view of effective descript...
Let $\De$ be a non-degenerate simplex on $k$ vertices. We prove that there exists a threshold $s_k<k...
We present strong versions of Marstrand's projection theorems and other related theorems. For exampl...
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real li...
We find sets naturally arising in Diophantine approximation whose Cartesian products exceed the expe...
Let A and B be Borel subsets of the Euclidean n-space with dim A + dim B > n and let 0 u for z in a...
Let A and B be Borel subsets of the Euclidean n-space with dim A + dim B > n. This is a survey on th...
For S-g(x, y) = x-g(y), x, y is an element of R-n, g is an element of O(n), we investigate the Lebes...
A classical theorem due to Mattila says that if A, B ⊂ ℝ d of Hausdorff dimension s A , s B respecti...
We give conditions on a general family P-lambda : R-n -> R-m, lambda is an element of Lambda of orth...
I shall discuss some recent developments on two closely related questions: How do projections affect...
l. Introilucti'on. Let m and n be positive integers with m < n and let O*(n, m) be the set o...
The Hausdorff dimension of a product $X\times Y$ can be strictly greater than that of $Y$, even when...
We prove some geometric properties of sets in the first Heisenberg group whose Heisenberg Hausdorff ...
This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets o...
In this paper, we study Hausdorff and Fourier dimension from the point of view of effective descript...
Let $\De$ be a non-degenerate simplex on $k$ vertices. We prove that there exists a threshold $s_k<k...
We present strong versions of Marstrand's projection theorems and other related theorems. For exampl...
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real li...
We find sets naturally arising in Diophantine approximation whose Cartesian products exceed the expe...