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Results tagged with cv.complex-variables
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user 5534
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
0
votes
2
answers
553
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Behavior of essential singularities in an 'open cone'
Picard's Big Theorem says that if a function $f(z)$ has an isolated essential singularity at a point $w$, then in every neighborhood of $w$, $f(z)$ hits every complex number infinitely many times, wit …
- 2,019
4
votes
1
answer
809
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Converse of Picard's Big Theorem?
The celebrated Big Theorem of Picard's is that, in every open set containing an essential singularity of a function $f(z)$, $f(z)$ takes on every value (except for at most one) of $\mathbb{C}$ infinit …
- 2,019
7
votes
2
answers
413
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Can curves induced by analytic maps wiggle infinitely across a line?
Let $f$ be a function analytic on an open subset $D\subset \mathbb{C}$, and let $\gamma:[0,1] \to D$ be a line segment. $g = f\circ\gamma$ is another curve in the complex plane; is it possible to for …
- 2,019