Hamilton: three-manifolds with positive Ricci curvature

What changed

Introduced and analyzed the Ricci-flow evolution equation to show that a compact three-manifold with positive Ricci curvature admits a metric of constant positive curvature.

Scientific scope

The record is the exact 1982 Journal of Differential Geometry paper. Later Ricci-flow singularity theory, Hamilton’s wider program and Perelman’s geometrization work 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 1982 Journal of Differential Geometry paper. Later Ricci-flow singularity theory, Hamilton’s wider program and Perelman’s geometrization work remain separate.

Contributors

• Richard S. Hamilton · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Hamilton positive Ricci curvature paper
• Crossref record for Hamilton 1982

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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