Displaying similar documents to “Stability of the Bishop familyοf holomorphic discs”

Some remarks on holomorphic extension in infinite dimensions

Pham Ban (1994)

Colloquium Mathematicae

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In finite-dimensional complex analysis, the extension of holomorphic maps has been investigated by many authors. In recent years some authors have considered this problem in the infinite-dimensional case. The aim of the present note is to study the extension of holomorphic maps with values in some Banach complex manifolds.

On proper discs in complex manifolds

Barbara Drinovec Drnovšek (2007)

Annales de l’institut Fourier

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Let X be a complex manifold of dimension at least 2 which has an exhaustion function whose Levi form has at each point at least 2 strictly positive eigenvalues. We construct proper holomorphic discs in X through any given point and in any given direction.

The fixed points of holomorphic maps on a convex domain

Do Duc Thai (1992)

Annales Polonici Mathematici

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We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in ℂ n then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

The Milnor number of functions on singular hypersurfaces

Mariusz Zając (1996)

Banach Center Publications

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The behaviour of a holomorphic map germ at a critical point has always been an important part of the singularity theory. It is generally known (cf. [5]) that we can associate an integer invariant - called the multiplicity - to each isolated critical point of a holomorphic function of many variables. Several years later it was noticed that similar invariants exist for function germs defined on isolated hypersurface singularities (see [1]). The present paper aims to show a simple approach...