Extremal discs and analytic continuation of product CR maps (Q2460984)

The main result of this paper is the following: Let \(M_1 \subset {\mathbb C}^n\) be a real analytic and strictly pseudoconvex generic manifold and let \(M_2\subset {\mathbb C}^n\) be a product of several real-analytic strictly convex hypersurfaces. Then every biholomorphic map taking an open subset in \(M_1\) to \(M_2\) continues along any path in \(M_1\) as a locally biholomorphic map. This result can be considered as an application of the theory of stationary discs attached to strictly pseudoconvex CR manifolds of higher codimension, developed by the second author in [Am. J. Math. 123, 445--473 (2001; Zbl 0995.32024)], and of the invariance under biholomorphisms of such special class of discs.