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Results tagged with several-complex-variables
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user 1811
4
votes
Accepted
connectedness holomorphically convex hull
The answer is no, unless you assume that $U$ is pseudoconvex. For example, take $K$ a unit circle. Then $\hat{K}_U$ will be the intersection of the unit disk with $U$. You can make it disconnected.
I …
- 2,263
8
votes
Accepted
zeros of holomorphic function in n variables
The conjecture is obviously false even for $n=2$. Check $f(z,w)=(w-z^2)(z-(w+1)^2)$. Write $z=x+iy$ and $w=u+iv$. Given $x$ and $u$, I can make first term zero unless $u>x^2$. I can make the second te …
- 2,263