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Conditional Uniformization of Kähler Surfaces
Abstract
We prove that a complete noncompact Kähler surface with nonnegative Ricci and nonnegative quadratic orthogonal bisectional curvature is contractible, and hence homeomorphic to ℝ4, if it is simply connected at infinity. Under positive bisectional curvature, this removes the contractibility assumption from the conditional uniformization theorem of Datar--Pingali--Seshadri: strong Steinness and simple connectivity at infinity suffice to identify the surface biholomorphically with ℂ2. We also derive bounded-gradient strictly plurisubharmonic exhaustions and uniform holomorphic kernel estimates for complete U(n)-invariant Kähler metrics on ℂn with nonnegative bisectional curvature.
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BibTeX
@misc{wu2026conditional,
title = {{Conditional Uniformization of Kähler Surfaces}},
author = {Jingcao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18506},
eprint = {2609.18506},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18506},
}
RIS
TY - UNPB
TI - Conditional Uniformization of Kähler Surfaces
AU - Jingcao Wu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18506
UR - https://arxiv.org/abs/2609.18506
AB - We prove that a complete noncompact Kähler surface with nonnegative Ricci and nonnegative quadratic orthogonal bisectional curvature is contractible, and hence homeomorphic to ℝ^4, if it is simply connected at infinity. Under positive bisectional curvature, this removes the contractibility assumption from the conditional uniformization theorem of Datar--Pingali--Seshadri: strong Steinness and simple connectivity at infinity suffice to identify the surface biholomorphically with ℂ^2. We also derive bounded-gradient strictly plurisubharmonic exhaustions and uniform holomorphic kernel estimates for complete U(n)-invariant Kähler metrics on ℂ^n with nonnegative bisectional curvature.
ER -