  We show that if $0<t<s\leq n-1$, $\Omega\subseteq \mathbb{R}^{n}$ with lower
$s$-content regular complement, and $z\in \Omega$, there is a chord-arc domain
$\Omega_{z}\subseteq \Omega $ with center $z$ so that
$\mathscr{H}^{t}_{\infty}(\partial\Omega_{z}\cap \partial\Omega)\gtrsim_{t}
\textrm{dist}(z,\Omega^{c})^{t}$. This was originally shown by Koskela, Nandi,
and Nicolau with John domains in place of chord-arc domains when $n=2$, $s=1$,
and $\Omega$ is a simply connected planar domain.
  Domains satisfying the conclusion of this result support $(p,\beta)$-Hardy
inequalities for $\beta<p-n+t$ by a result of Koskela and Lehrb\"{a}ck;
Lehrb\"{a}ck also showed that $s$-content regularity of the complement for some
$s>n-p+\beta$ was necessary. Thus, the combination of these results gives a
characterization of which domains support pointwise $(p,\beta)$-Hardy
inequalities for $\beta<p-1$ in terms of lower content regularity.

Metric Geometry;Analysis of PDEs;Classical Analysis and ODEs