Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a planar variant of the Kakeya problem   A K^n_2-set is a set of zero Lebesgue measure containing a translate of every
plane in an (n-2)-dimensional manifold in Gr(n,2), where the manifold fulfills
a curvature condition. We show that this is a natural class of sets with
respect to the Kakeya problem and prove that dim_H(E)\ge 7/2 for all K^4_2-sets
E. When the underlying field is replaced by the complex numbers C, we get
dim_H(E)\ge 7 for all K^4_2-sets over C, and we construct an example to show
that this is sharp. Thus K^4_2-sets over C do not necessarily have full
Hausdorff dimension.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics