Questions tagged [holomorphic-maps]

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2 votes
1 answer

Singularity on the boundary of domain of holomorphy

Let $\phi$ be a continuous function on the closed upper half-plane $\{ z\in\mathbb{C}: \operatorname{Im}(z)\ge 0\}$ and holomorphic in the interior. Suppose that the function $x\phi(x)$ is in $C^1(\...
5 votes
1 answer

Does there exist a study of entire functions which satisfy $|F(x+iy)| \leq a e^{-bx^2}e^{cy^2}$?

I recently successfully extended a certain result where I use analytic functions which satisfy the following property: $F: \mathbb C \to \mathbb C$ is entire and there exist constants $a,b,c>0$ ...
4 votes
2 answers

Geometry of critical points of holomorphic maps in projective space

Let $f:\mathbb{CP}^n\to\mathbb{CP}^n$ be a holomorphic map; I am interested in what the subvariety of critical points could be. More specifically, let $J=\{p\in \mathbb{CP}^n\ :\ \det\mathrm{Jac}(f)=0\...