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Content archived on 2022-12-23

Complex analysis and geometry

Objective



Very little is known about the boundary values of the proper holomorphic functions on weakly pseudo-convex domains. When these domains satisfy certain geometrical invariant properties (Reinhardt domains, convex domains), the action of a group of automorphisms attempts to estimate more precisely the value of the Jacobian with respect to the boundary distance to give a generalization of known properties in the strictly pseudo-convex case.

The expected results are a description of the properties of the normal and tangent ranks of C.R. mappings; elimination of L1-singularities of Hölder pick sets of C.R. mappings; classification of proper holomorphic mappings between bounded complete Reinhardt domains in C{2} and splitting of a proper holomorphic mapping; description of good domains where every proper holomorphic self-map is an automorphism; characterization of C.R. homeomorphisms; and Weierstrass division theorems.

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Coordinator

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE
EU contribution
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Participants (8)

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