On peak-interpolation manifolds for $\boldsymbol{A}\boldsymbol{(}\boldsymbol{\Omega}\boldsymbol{)}$ for convex domains in $\boldsymbol{\mathbb{C} }^{\boldsymbol{n}}$

Let $\Omega$ be a bounded, weakly convex domain in ${\mathbb{C} }^n$, $n\geq 2$, having real-analytic boundary. $A(\Omega)$ is the algebra of all functions holomorphic in $\Omega$ and continuous up to the boundary. A submanifold $\boldsymbol{M}\subset \partial \Omega$ is said to be complex-tangential if $T_p(\boldsymbol{M})$ lies in the maximal complex subspace of $T_p(\partial \Omega)$ for each $p\in\boldsymbol{M}$. We show that for real-analytic submanifolds $\boldsymbol{M}\subset\partial \Omega$, if $\boldsymbol{M}$ is complex-tangential, then every compact subset of $\boldsymbol{M}$ is a peak-interpolation set for $A(\Omega)$.