### Abstract

Let X be a Stein manifold, dimC X ≥ 2, K a compact subset of X, and ω an open subset of X containing K such that ω\K is connected. Suppose that ω\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. ω, such that V/K is connected and H^{2} (V,R) = 0, then K is a complex analytic subvariety of X, hence reduced to a finite number of points.

Original language | English |
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Pages (from-to) | 3037-3044 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2009 |

### Fingerprint

### Keywords

- Analyticity of compact sets
- Complete Kähler metrics
- Stein manifolds

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Analyticity of compact complements of complete kähler manifolds.** / Anchouche, Boudjemâa.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 137, no. 9, pp. 3037-3044. https://doi.org/10.1090/S0002-9939-09-09762-7

}

TY - JOUR

T1 - Analyticity of compact complements of complete kähler manifolds

AU - Anchouche, Boudjemâa

PY - 2009/9

Y1 - 2009/9

N2 - Let X be a Stein manifold, dimC X ≥ 2, K a compact subset of X, and ω an open subset of X containing K such that ω\K is connected. Suppose that ω\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. ω, such that V/K is connected and H2 (V,R) = 0, then K is a complex analytic subvariety of X, hence reduced to a finite number of points.

AB - Let X be a Stein manifold, dimC X ≥ 2, K a compact subset of X, and ω an open subset of X containing K such that ω\K is connected. Suppose that ω\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. ω, such that V/K is connected and H2 (V,R) = 0, then K is a complex analytic subvariety of X, hence reduced to a finite number of points.

KW - Analyticity of compact sets

KW - Complete Kähler metrics

KW - Stein manifolds

UR - http://www.scopus.com/inward/record.url?scp=77951066358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951066358&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-09-09762-7

DO - 10.1090/S0002-9939-09-09762-7

M3 - Article

VL - 137

SP - 3037

EP - 3044

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -