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arxiv: 1505.07521 · v2 · submitted 2015-05-28 · 🧮 math.DG · math.CV

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Gromov-Hausdorff limits of K\"ahler manifolds with bisectional curvature lower bound I

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classification 🧮 math.DG math.CV
keywords complexahleranalyticbisectionalboundcurvaturegromov-hausdorfflimit
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Given a sequence of complete(compact or noncompact) K\"ahler manifolds $M^n_i$ with bisectional curvature lower bound and noncollapsed volume, we prove that the pointed Gromov-Hausdorff limit is homeomorphic to a normal complex analytic space. The complex analytic structure is the natural "limit" of complex structure of $M_i$.

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