密象全纯映射的逼近和积累结果

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2022-11-10 DOI:10.7146/math.scand.a-136450

Giovanni Domenico Di Salvo

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引用次数: 0

摘要

我们给出了流形值映射的四个近似定理。第一个用具有稠密图像的全纯嵌入逼近$\mathbb｛C｝^n$中伪凸域上的全纯嵌。第二个定理用具有稠密映象的全纯映象逼近具有有界映象的复流形上的全纯映射。最后两个定理以另一种方式工作，（在不同的设置中）构造全纯映射序列（第一个中的嵌入），收敛到在给定紧致上定义的稠密图像减去某些点的映射（因此通常不是全纯的）。

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Approximation and accumulation results of holomorphic mappings with dense image

We present four approximation theorems for manifold–valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\mathbb{C}^n$ with holomorphic embeddings with dense images. The second theorem approximates holomorphic mappings on complex manifolds with bounded images with holomorphic mappings with dense images. The last two theorems work the other way around, constructing (in different settings) sequences of holomorphic mappings (embeddings in the first one) converging to a mapping with dense image defined on a given compact minus certain points (thus in general not holomorphic).

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.