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# A Real-analytic Nonpolynomially Convex Isotropic Torus with No Attached Discs

Published:2017-06-07
Printed: Jun 2018
• Purvi Gupta,
Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada
 Format: LaTeX MathJax PDF

## Abstract

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
 MSC Classifications: 32V40 - Real submanifolds in complex manifolds 32E20 - Polynomial convexity 53D12 - Lagrangian submanifolds; Maslov index

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