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The fixed points of holomorphic maps on a convex domain

Do Duc Thai — 1992

Annales Polonici Mathematici

We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in 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.

Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group

Do Duc ThaiDinh Huy Hoang — 1999

Annales Polonici Mathematici

We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection π 1 : V Γ is finite and proper, then R V : O ( Γ × G ) I m R V O ( V ) has a right inverse

Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Do Duc ThaiNguyen Huu Kien — 2015

Acta Arithmetica

The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety V k ̅ m , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety V m .

On D*-extension property of the Hartogs domains.

Do Duc ThaiPascal J. Thomas — 2001

Publicacions Matemàtiques

A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is pseudoconvex,...

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