Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension conservation for self-similar sets and fractal percolation   We introduce a technique that uses projection properties of fractal
percolation to establish dimension conservation results for sections of
deterministic self-similar sets. For example, let $K$ be a self-similar subset
of $\mathbb{R}^2$ with Hausdorff dimension $\dim_H K >1$ such that the
rotational components of the underlying similarities generate the full rotation
group. Then for all $\epsilon >0$, writing $\pi_\theta$ for projection onto the
line $L_\theta$ in direction $\theta$, the Hausdorff dimensions of the sections
satisfy $\dim_H (K\cap \pi_\theta^{-1}x)> \dim_H K - 1 - \epsilon$ for a set of
$x \in L_\theta$ of positive Lebesgue measure, for all directions $\theta$
except for those in a set of Hausdorff dimension 0. For a class of self-similar
sets we obtain a similar conclusion for all directions, but with lower box
dimension replacing Hausdorff dimensions of sections. We obtain similar
inequalities for the dimensions of sections of Mandelbrot percolation sets.

8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th