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Gromov hyperbolicity of strongly pseudoconvex almost complex manifolds


Authors: Florian Bertrand and Hervé Gaussier
Journal: Proc. Amer. Math. Soc. 143 (2015), 3901-3913
MSC (2010): Primary 32Q45, 32Q60, 32T15, 58E05
DOI: https://doi.org/10.1090/proc/12564
Published electronically: April 16, 2015
MathSciNet review: 3359581
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Abstract: Let $ D=\{\rho < 0\}$ be a smooth relatively compact domain in an almost complex manifold $ (M,J)$, where $ \rho $ is a smooth defining function of $ D$, strictly $ J$-plurisubharmonic in a neighborhood of the closure $ \overline {D}$ of $ D$. We prove that $ D$ has a connected boundary and is Gromov hyperbolic.


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Additional Information

Florian Bertrand
Affiliation: Department of Mathematics, University of Vienna, Nordbergstrasse 15, Vienna, 1090, Austria
Address at time of publication: Department of Mathematics, American University of Beirut, Beirut, Lebanon
Email: fb31@aub.edu.lb

Hervé Gaussier
Affiliation: UJF-Grenoble 1, Institut Fourier, Grenoble, F-38402, France — and — CNRS UMR 5582, Institut Fourier, Grenoble, F-38041, France
Address at time of publication: University of Grenoble Alpes, IF, F-38000 Grenoble, France — and — CNRS, IF, F-38000 Grenoble, France
Email: herve.gaussier@ujf-grenoble.fr

DOI: https://doi.org/10.1090/proc/12564
Keywords: Almost complex manifold, Gromov hyperbolicity, Kobayashi hyperbolicity, Morse theory
Received by editor(s): May 6, 2014
Published electronically: April 16, 2015
Additional Notes: The research of the first author was supported by FWF grants AY0037721 and M1461-N25.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society

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