Proves normalized growth estimates and a sharp 8π(1-AVR) scalar-curvature flux bound for noncompact manifolds with nonnegative Ricci curvature, confirming and refining a 3D conjecture.
A note on the Gaussian curvature on noncompact surfaces
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abstract
We give a short proof of the following fact. Let $\Sigma$ be a connected, finitely connected, noncompact manifold without boundary. If $g$ is a complete Riemannian metric on $\Sigma$ whose Gaussian curvature $K$ is nonnegative at infinity, then $K$ must be integrable. In particular, we obtain a new short proof of the fact that if $\Sigma$ admits a complete metric whose Gaussian curvature is nonnegative and positive at one point, then $\Sigma$ is diffeomorphic to $\mathbb{R}^2$.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Cohn--Vossen-Type Inequalities for Three-Manifolds and Locally Conformally Flat Manifolds
Proves normalized growth estimates and a sharp 8π(1-AVR) scalar-curvature flux bound for noncompact manifolds with nonnegative Ricci curvature, confirming and refining a 3D conjecture.