ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 32, 22, 14 Zaitsev, Dmitri, Universität Tüebingen On holomorphic boundary extensions, web theory and invariants of Grassmanians. For D, D′ analytic polyhedra in ℂ^{n}, we prove that a biholomorphic mapping f: D → D′ extends holomorphically to a dense boundary subset under a certain condition of general position. This result can be extended to a more general class of domains with no smoothness condition on the boundary. We use the invariance of the so-called characteristic webs in the sense of Remmert-Stein and calculate invariants of Grassmanian products G_{n,n_{1}} × ⋯ × G_{n,n_{s}} under the diagonal action of GL_{n} to derive partial differential equations for f. Holomorphic extensions of these equations can be exploited to extend f. Reference: D. Zaitsev, Domains of polyhedral type and boundary extensions of biholomorphisms, to appear in Indiana Math. Journal, 1998.