STATIONARY DISCS OF FIBRATIONS OVER THE CIRCLE

Abstract

Stationary discs of fibrations over the unit circle ∂D are considered. It is shown that if all fibers of a fibration Σ⊆∂D×Cn over the unit circle ∂D are strongly pseudoconvex hypersurfaces in Cn, then for every stationary disc f of the fibration Σ one can define the partial indices of f. In the case all fibers of Σ are strictly convex, it is proved that all partial indices of a stationary disc f are 0. It is also proved that in the case a stationary disc f of the fibration Σ is non-degenerate, the only possible partial indices of f are 0, 1 and –1. In particular, these results give information on the polynomial hull of Σ and new proofs of results related to the smoothness of the Kobayashi metric on some strongly pseudoconvex domains in Cn.