Let $V$ be an analytic subvariety of a domain $\Omega$ in $\mathbb{C}^{n}$. When does $V$ have the property that every bounded holomorphic function $f$ on $V$ has an extension to a bounded holomorphic function on $\Omega$ with the same norm?
An obvious sufficient condition is if $V$ is a holomorphic retract of $\Omega$. We shall discuss for what domains $\Omega$ this is also necessary.
This is joint work with Łukasz Kosiński.