Analyticity of compact complements of complete kähler manifolds

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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 H2 (V,R) = 0, then K is a complex analytic subvariety of X, hence reduced to a finite number of points.

Original languageEnglish
Pages (from-to)3037-3044
Number of pages8
JournalProceedings of the American Mathematical Society
Volume137
Issue number9
DOIs
Publication statusPublished - Sep 2009

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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