Degree reduction and graininess for Kakeya-type sets in $\mathbb R^3$
نویسندگان
چکیده
منابع مشابه
Kakeya-type sets in finite vector spaces
For a finite vector space V and a non-negative integer r ≤ dim V we estimate the smallest possible size of a subset of V , containing a translate of every rdimensional subspace. In particular, we show that if K ⊆ V is the smallest subset with this property, n denotes the dimension of V , and q is the size of the underlying field, then for r bounded and r < n ≤ rq we have |V \K| = Θ(nq); this im...
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In this paper we investigate an analogue for curves of the famous Kakeya conjecture about straight lines. The simplest version of the latter asks whether a set in R that includes a unit line segment in every direction must necessarily have dimension n. The analogue we have in mind replaces the line segments by curved arcs from a specified family. (This is a quite different problem from that con...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2016
ISSN: 0213-2230
DOI: 10.4171/rmi/891