We give conditions for k‐point configuration sets of thin sets to have nonempty interior,
applicable to a wide variety of configurations. This is a continuation of our earlier work (J …

We prove new results of Mattila–Sjölin type, giving lower bounds on Hausdorff dimensions
of thin sets E⊂ R d ensuring that various k-point configuration sets, generated by elements …

In this paper we show that if a compact set E⊂ R d, d≥ 3, has Hausdorff dimension greater
than (4 k-1) 4 kd+ 1 4 when 3≤ d< k (k+ 3)(k-1) or d-1 k-1 when k (k+ 3)(k-1)≤ d, then the …

We introduce a class of Falconer distance problems, which we call of restricted type, lying
between the classical version and its pinned variant. Prototypical restricted distance sets are …

We generalize a result of McDonald and Taylor which concerns the size of the tuples of
edge lengths in the set $ C_1\times C_2 $ utilizing the notion of thickness. Specifically, we …

Abstract Let ϕ (x, y): ℝ d× ℝ d→ ℝ ϕ(x,y):R^d*R^d→R be a function. We say ϕ is a Mattila–
Sjölin type function of index γ if γ is the smallest number satisfying the property that for any …

In this paper, we study the Erdös--Falconer distance problem in five dimensions for sets of
Cartesian product structures. More precisely, we show that for A⊂F_p with |A|≫p^1322 …

Let f∈ R [x, y, z] be a quadratic polynomial that depends on each variable and that does not
have the form g (h (x)+ k (y)+ l (z)). Let A, B, C be compact sets in R. Suppose that dim …

This dissertation contains work from the author's papers [35] and [36] with coauthor Eyvindur
Palsson. The classic Mattila-Sjolin theorem shows that if a compact subset of mathbbRd has …

Construction of a Mattila--Sj\\\{o}lin type function over a finite field - 대한수학회지 - 대한수학회
: 논문 - DBpia 메뉴 건너뛰기 DBpia 전체 search 검색하기 상세검색 idea 리포트/논문 작성을 …