Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\varepsilon$-Approximability of Harmonic Functions in $L^p$ Implies
  Uniform Rectifiability   Suppose that $\Omega \subset \mathbb{R}^{n+1}$, $n \ge 2$, is an open set
satisfying the corkscrew condition with an $n$-dimensional ADR boundary,
$\partial \Omega$. In this note, we show that if harmonic functions are
$\varepsilon$-approximable in $L^p$ for any $p > n/(n-1)$, then $\partial
\Omega$ is uniformly rectifiable. Combining our results with those in [HT]
(Hofmann-Tapiola) gives us a new characterization of uniform rectifiability
which complements the recent results in [HMM] (Hofmann-Martell-Mayboroda),
[GMT] (Garnett-Mourgoglou-Tolsa) and [AGMT] (Azzam-Garnett-Mourgoglou-Tolsa).

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The categories of this paper are: eess
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys