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arXiv · 2605.31477

Nonnegative Ricci Curvature and Uniformly Convex Boundary Forces Compactness

Zetian Yan·Xingyu Zhu
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Abstract

We confirm a compactness conjecture of M. Li. If a complete Riemannian manifold has nonnegative Ricci curvature and uniformly convex boundary in the sense that the second fundamental form satisfies $h\ge1$. Then we prove it is compact, and consequently has finite fundamental group. The proof uses monotone quantities constructed via positive proper harmonic functions with Neumann condition.

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Zetian Yan, Xingyu Zhu. 2026-05-29. Nonnegative Ricci Curvature and Uniformly Convex Boundary Forces Compactness. https://arxiv.org/abs/2605.31477

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