Gromov hyperbolicity of strongly pseudoconvex almost complex manifolds
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- by Florian Bertrand and Hervé Gaussier PDF
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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.References
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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
- MR Author ID: 821365
- 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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3901-3913
- MSC (2010): Primary 32Q45, 32Q60, 32T15, 58E05
- DOI: https://doi.org/10.1090/proc/12564
- MathSciNet review: 3359581