Analyticity of compact complements of complete Kähler manifolds
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Abstract:
Let $X$ be a Stein manifold, $\dim _{\mathbb {C}}X\geq 2$, $K$ a compact subset of $X$, and $\Omega$ an open subset of $X$ containing $K$ such that $\Omega \diagdown K$ is connected. Suppose that $\Omega \diagdown K$ carries a complete Kähler metric of bounded bisectional curvature, and locally of finite volume near $K$. If $K$ admits a Stein neighborhood $V$, $V\subseteq \Omega$, such that $V\diagdown K$ is connected and $H^{2}\left ( V,\mathbb {R}\right ) =0,$ then $K$ is a complex analytic subvariety of $X,$ hence reduced to a finite number of points.References
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Additional Information
- Boudjemâa Anchouche
- Affiliation: Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman
- Email: anchouch@squ.edu.om
- Received by editor(s): October 10, 2007
- Received by editor(s) in revised form: July 18, 2008, and November 10, 2008
- Published electronically: March 24, 2009
- Communicated by: Mei-Chi Shaw
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3037-3044
- MSC (2000): Primary 32T05, 32Q15
- DOI: https://doi.org/10.1090/S0002-9939-09-09762-7
- MathSciNet review: 2506462