Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolute continuity of the harmonic measure on low dimensional
  rectifiable sets   We consider a uniformly rectifiable set $\Gamma \subset \mathbb R^n$ of
dimension $d<n-1$. By using degenerate elliptic operators on the complement
$\Omega = \mathbb R^n \setminus \Gamma$, Guy David, Svitlana Mayboroda, and the
author introduced a notion of harmonic measure on $\Gamma$.
  We prove in the present article that this harmonic measure on $\Gamma$
satisfies the $A^\infty$-property, that is the harmonic measure and the
$d$-dimension Hausdorff measure on $\Gamma$ are mutually absolutely continuous
in a quantitative and scale invariant way. Thus, we give an alternate proof of
a recent theorem of David and Mayboroda, which itself extends a result of
Hofmann and Martell to the case where the uniformly rectifiable set $\Gamma$ is
not of codimension 1.
  The proof is surprisingly simple - in particular does not follow the route
used by David and Mayboroda, or by Hofmann and Martell - but is specific to the
case when $d<n-1$.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an