Gromov-Hausdorff limits of Kähler manifolds with bisectional curvature lower bound I

Abstract

Given a sequence of complete(compact or noncompact) Kähler manifolds $M_i^n$ 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 $M_i$.

26 pages

References in corpus (1)

• Regularity of Einstein Manifolds and the Codimension 4 Conjecture

Cited by in corpus (2)

• Chern-Ricci flows on noncompact complex manifolds
• A note on existence of exhaustion functions and its applications