On the dimension of the set of extremal discs for a CR manifold of codimension two (Q868756)

From the introduction: \textit{L. Lempert} [Bull. Soc. Math. Fr. 109, 427--474 (1981; Zbl 0492.32025)] introduced extremal discs for a convex domain in \(\mathbb C^n\), a very productive notion which had many applications. \textit{A. Tumanov} [Am. J. Math. 123, No.~3, 445--473 (2001; Zbl 0995.32024)] introduced a local theory of extremal discs attached to a real strictly pseudoconvex manifold of higher codimension. For a hypersurface, his discs coincide with those of Lempert. An important feature of extremal discs for a hypersurface is that of stability under small perturbations. In particular, the dimension of the set of extremal discs depends only on the dimension of the ambient space. We show that this property is significantly violated in higher codimension.