Yau's uniformization conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Yau's uniformization conjecture

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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If this game doesn't work on your computer, we can't help you. No Lean version yet. Some unformalized games could have issues!

expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	curvy surfaces	Levels:	1
Category:	Differential geometry	Lean version:	not yet
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Yau's uniformization conjecture. 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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LEVEL 1 Uniformization of complete Kähler manifolds with positive bisectional curvature

released 2026-09-23 | 3 theorems · 18 lemmas · 29 proofs · 35,045 words | PLAY LEVEL 1 » (pdf)

We prove that every complete connected noncompact Kähler manifold with strictly positive holomorphic bisectional curvature is biholomorphic to complex Euclidean space. This resolves Yau's uniformization conjecture positively in every complex dimension.

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