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Search: MSC category 32E20 ( Polynomial convexity )

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1. CMB Online first

Gupta, Purvi
A real-analytic nonpolynomially convex isotropic torus with no attached discs
We show by means of an example in $\mathbb C^3$ that Gromov's theorem on the presence of attached holomorphic discs for compact Lagrangian manifolds is not true in the subcritical real-analytic case, even in the absence of an obvious obstruction, i.e, polynomial convexity.

Keywords:polynomial hull, isotropic submanifold, holomorphic disc
Categories:32V40, 32E20, 53D12

2. CMB Online first

Bayart, Frédéric; Gauthier, Paul M
Functions universal for all translation operators in several complex variables
We prove the existence of a (in fact many) holomorphic function $f$ in $\mathbb{C}^d$ such that, for any $a\neq 0$, its translations $f(\cdot+na)$ are dense in $H(\mathbb{C}^d)$.

Keywords:hypercyclic operator, translation operator
Categories:47A16, 32E20

3. CMB 2010 (vol 54 pp. 370)

Stout, Edgar Lee
Manifold-Valued Holomorphic Approximation
This note considers the problem of approximating continuous maps from sets in complex spaces into complex manifolds by holomorphic maps.

Category:32E20

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