Yau: Ricci curvature and the complex Monge–Ampère equation

What changed

Solved the prescribed-Ricci-form problem for compact Kähler manifolds through the complex Monge–Ampère equation, establishing the Calabi conjecture in the stated setting.

Scientific scope

The record is the exact 1978 Communications on Pure and Applied Mathematics paper. Calabi’s conjecture, later extensions, applications to Calabi–Yau manifolds and string theory remain separate.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact 1978 Communications on Pure and Applied Mathematics paper. Calabi’s conjecture, later extensions, applications to Calabi–Yau manifolds and string theory remain separate.

Contributors

• Shing-Tung Yau · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Yau, Ricci curvature and the complex Monge–Ampère equation
• Shing-Tung Yau publication list

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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