Recent zbMATH articles in MSC 30G30 https://www.zbmath.org/atom/cc/30G30 2022-05-16T20:40:13.078697Z Werkzeug Open and surjective mapping theorems for differentiable maps with critical points https://www.zbmath.org/1483.26012 2022-05-16T20:40:13.078697Z "Li, Liangpan" https://www.zbmath.org/authors/?q=ai:li.liangpan Summary: Let $$\Omega$$ be an open subset of $$\mathbb R^n$$ $$(n \ge 2)$$, and let $$F : \Omega \rightarrow \mathbb R^n$$ be a continuously differentiable map with countably many critical points. We show that $$F$$ is an open map. Let $$G :\mathbb R^n \rightarrow \mathbb R^n$$ $$(n \ge 1)$$ be a continuously differentiable map such that $$G(x) \rightarrow \infty$$ as $$x \rightarrow \infty$$. Then it is proved that $$G$$ is surjective if and only if each connected component of the complement of the set of critical values of $$G$$ contains at least one image of $$G$$. Several applications of both theorems especially to complex analysis are presented. $$q$$-analyticity in the sense of Ahern \& Bruna https://www.zbmath.org/1483.32003 2022-05-16T20:40:13.078697Z "Daghighi, Abtin" https://www.zbmath.org/authors/?q=ai:daghighi.abtin Summary: We consider an alternative notion of polyanalyticity in several complex variables based upon a previous work of \textit{P. Ahern} and \textit{J. Bruna} [Rev. Mat. Iberoam. 4, No. 1, 123--153 (1988; Zbl 0685.42008)]. We also generalize this notion to the case of generic embedded submanifolds of $$\mathbb{C}^n$$ and give characterizations of the notions involved.