Holomorphic mapping

In the case of dimension one, this problem was studied by Lappan and Hinkkanen. The main purpose of this paper is to extend the result of Tan in to the case of hypersurface targets. Our result is also the counterpart of the result of Son and Tan in on the normality criterion of holomorphic mappings.

5p visharma 20-10-2023 7 2   Download

Part 1 of ebook "Holomorphic functions and integral representations in several complex variables" provides readers with contents including: elementary local properties of holomorphic functions; domains of holomorphy and pseudoconvexity; differential forms and hermitian geometry; integral representations in Cn;...

206p lytamnguyet 04-08-2023 3 3   Download

In the paper "Some properties of Reinhardt domains", the authors establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, the authors give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk ∆∗ into D can be extended holomorphically to a map from ∆ into D.

15p runordie5 04-07-2022 9 2   Download

The aim of the present note "Holomorphic maps of uniform type" is to find some necessary and sufficient conditions for the equality (UN) \(H\left( {E,{\rm{ }}X} \right){\rm{ }} = {\rm{ }}{H_u}\left( {E,{\rm{ }}X} \right)\) to hold. This problem for vector-valued holomorphic maps, i.e. for the case where X is a locally convex space, was investigated by some authors. The first result on this problem belongs to Colombeau and Mujica.

6p runordie5 04-07-2022 12 2   Download

The main aim of this article “On the kahlerity of complex spaces having the hartogs extension property” is to show that there exists a non-Kählerian complex manifold Z such that every separately holomorphic mapping \(f:C \times C \to Z\) is jointly holomorphic, but Z does not have (HEP). This is an affirmative answer to the conjecture posed in [4, Remark 5.1(2)].

4p runordie5 04-07-2022 11 2   Download

Mục đích của bài luận văn là nghiên cứu một số tính chất của lớp các hàm số triệt tiêu cấp vô hạn và ứng dụng của chúng trong bài toán về sự tồn tại trường vectơ chỉnh hình tiếp xúc. Luận văn trình bày lại một số kết quả trong bài báo “A note on uniqueness boundary of holomorphic mappings” của các tác giả Ninh Văn Thu, Nguyễn Ngọc Khanh và tiền ấn phẩm “On the nonexistence of nontrivial tangential holomorphic vector fields of a certain hypersurface of infinite type” của tác giả Ninh Văn Thu.

28p capheviahe26 02-02-2021 21 1   Download

The notions of hyperbolicity and tautness modulo an analytic subset of complex spaces are due to S. Kobayashi. Much attention has been given to these notions, and the results on this problem can be applied to many areas of mathematics, in particular to the extensions of holomorphic mappings. The main goal of this article is to give necessary and sufficient conditions on the hyperbolicity or tautness modulo an analytic subset of complex spaces.

10p tamynhan5 10-12-2020 11 2   Download

In this paper, we establish a second main theorem for holomorphic mappings from a disc (R) into Pn(C) and families of hyperplanes in subgeneral position. Our result is an extension the classical second main theorem of Cartan-Nochka and the second main theorem of Fujimoto.

9p tamynhan9 02-12-2020 10 3   Download

Conformal Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, namely conformal invariant Riemannian maps, holomorphic conformal Riemannian maps, and conformal antiinvariant Riemannian maps, are introduced.

16p nutifooddau 21-01-2019 20 2   Download

We characterize transversality, non-transversality properties on the moduli space of genus 0 stable maps to a rational projective surface. If a target space is equipped with a real structure, i.e, anti-holomorphic involution, then the results have real enumerative applications.

32p danhdanh27 07-01-2019 11 1   Download

In this article, we study the ramification of the holomorphic map ramificate over hyperplanes in nsubgeneral position in ( ) k . This work is a continuation of previous work of Dethloff-Ha [1]. We thus give an improvement of the results by studying the holomorphic maps with ramification of M. Ru [3] and Dethloff-Ha.

5p blackwidow123 15-06-2018 28 2   Download

Given a holomorphic vector bundle E over a compact K¨hler manifold X, a one defines twisted Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f : Σ → X with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle H 0 (Σ, f ∗ E) H 1 (Σ, f ∗ E). Using the formalism of quantized quadratic Hamiltonians [25], we express the descendant potential for the twisted theory in terms of that for X. ...

40p noel_noel 17-01-2013 56 7   Download

We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y . Introduction Motivated by the seminal works of Oka [40] and Grauert ([24], [25], [26]) we say that a complex manifold Y enjoys the Oka property if for every Stein manifold X, every compact O(X)-convex subset K of X and every continuous map f0 : X → Y which is holomorphic in an...

20p noel_noel 17-01-2013 50 5   Download

In the symplectic category there is a ‘connect sum’ operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z = X#Y in terms of the relative GW invariants of X and Y . Several applications to enumerative geometry are given. Gromov-Witten invariants are counts of holomorphic maps into symplectic manifolds.

92p tuanloccuoi 04-01-2013 44 7   Download

The usual index theorems for holomorphic self-maps, like for instance the classical holomorphic Lefschetz theorem (see, e.g., [GH]), assume that the fixed-points set contains only isolated points. The aim of this paper, on the contrary, is to prove index theorems for holomorphic self-maps having a positive dimensional fixed-points set. The origin of our interest in this problem lies in holomorphic dynamics.

47p tuanloccuoi 04-01-2013 49 6   Download

The book before the reader is devoted to an exposition of results of investigations carried out mainly over the last 10-15 years concerning certain questions in the theory of quasiconformal mappings. The principal objects of investigation-mappings with bounded distortion- are a kind of n-space analogue of holomorphic functions. As is known, every holomorphic function is characterized geometrically by the fact that the niapping of a planar domain it implements is conformal. In the n-space case the condition of conformality singles out a very narrow class of mappings.

380p hotmoingay 04-01-2013 36 3   Download