  In this paper, we prove that: if $\kappa$ is supercompact and the
$\mathsf{HOD}$ Hypothesis holds, then there is a proper class of regular
cardinals in $V_{\kappa}$ which are measurable in $\mathsf{HOD}$. Woodin also
proved this result. As a corollary, we prove Woodin's Local Universality
Theorem. This work shows that under the assumption of the $\mathsf{HOD}$
Hypothesis and supercompact cardinals, large cardinals in $\mathsf{V}$ are
reflected to be large cardinals in $\mathsf{HOD}$ in a local way, and reveals
the huge difference between $\mathsf{HOD}$-supercompact cardinals and
supercompact cardinals under the $\mathsf{HOD}$ Hypothesis.
