A Simplification and Extension of Fefferman's Theorem on Biholomorphic Mappings.
Let be the open unit ball of a Banach space , and let be a holomorphic map with . In this paper, we discuss a condition whereby is a linear isometry on .
Here we show that a Kupka component of a codimension 1 singular foliation of with not a square is a complete intersection. The result implies the existence of a meromorphic first integral of .
Here we show that a Kupka component of a codimension 1 singular foliation of is a complete intersection. The result implies the existence of a meromorphic first integral of . The result was previously known if was assumed to be not a square.
To a germ with one-dimensional singular locus one associates series of isolated singularities , where l is a general linear function and . We prove an attaching result of Iomdin-Lê type which compares the homotopy types of the Milnor fibres of and f. This is a refinement of the Iomdin-Lê theorem in the general setting of a singular underlying space.
In this survey we give geometric interpretations of some standard results on boundary behaviour of holomorphic self-maps in the unit disc of ℂ and generalize them to holomorphic self-maps of some particular domains of ℂⁿ.