2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73714Let $S$ be a real-analytic hypersurface in $C^n$ or, more generally, a CR-submanifold in a complex manifold $Z$ of arbitrary CR-codimension. This paper addresses the question, when a local biholomorphic map between open sets in $Z$ sending an open piece of $S$ into $S$ extends to a global biholomorphic self-map of $Z$ preserving $S$. We give answers for a large class of Levi-degenerate group orbits in compact Hermitian symmetric spaces.Complex Variables17C50, 22F30, 32M15, 32V25, 32V35text