Recent zbMATH articles in MSC 30G30https://www.zbmath.org/atom/cc/30G302022-05-16T20:40:13.078697ZWerkzeugOpen and surjective mapping theorems for differentiable maps with critical pointshttps://www.zbmath.org/1483.260122022-05-16T20:40:13.078697Z"Li, Liangpan"https://www.zbmath.org/authors/?q=ai:li.liangpanSummary: 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 \& Brunahttps://www.zbmath.org/1483.320032022-05-16T20:40:13.078697Z"Daghighi, Abtin"https://www.zbmath.org/authors/?q=ai:daghighi.abtinSummary: 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.