  Let Y be a regular covering of a complex projective manifold M\hookrightarrow
CP^{N} of dimension n\geq 2. Let C be intersection with M of at most n-1
generic hypersurfaces of degree d in CP^{N}. The preimage X of C in Y is a
connected submanifold. Let H^{\infty}(Y) and H^{\infty}(X) be the Banach spaces
of bounded holomorphic functions on Y and X in the corresponding supremum
norms. We prove that the restriction H^{\infty}(Y)\longrightarrow H^{\infty}(X)
is an isometry for d large enough. This answers the question posed in [L] by F.
Larusson and strengthen his example of the Riemann surface with large corona.
