Proves Yau’s uniformization conjecture: every complete connected noncompact Kähler manifold with strictly positive holomorphic bisectional curvature is biholomorphic to ℂn.
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The paper states
In Uniformization of complete Kähler manifolds with positive bisectional curvature
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Let M be a connected noncompact complex manifold of complex dimension n\geq1. If M admits a smooth complete Kähler metric with strictly positive holomorphic bisectional curvature, then M is biholomorphic to \C^n.
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Ved Datar, Vamsi Pritham Pingali, Harish Seshadri, Positive bisectional curvature, Ricci mass, and the fundamental group, 7 October 2026. Source
Datar, Pingali and Seshadri say OpenAI’s all-dimension proof of Yau’s uniformisation conjecture uses a quite different approach from theirs, and that their finiteness theorem remains new.
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Why this passage is shown
Theorem 1.1
In Uniformization of complete Kähler manifolds with positive bisectional curvature