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arXiv · 2505.10520

Sharp integral bound of scalar curvature on $3$-manifolds

Ovidiu Munteanu·Jiaping Wang
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Abstract

It is shown that the integral of the scalar curvature on a geodesic ball of radius $R$ in a three-dimensional complete manifold with nonnegative Ricci curvature is bounded above by $8\pi R$ asymptotically for large $R$ provided that the scalar curvature is bounded between two positive constants.

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Ovidiu Munteanu, Jiaping Wang. 2025-05-15. Sharp integral bound of scalar curvature on $3$-manifolds. https://arxiv.org/abs/2505.10520

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