arXiv:2505.10520 Abstract | arXiv Analytics

arXiv:2505.10520 [math.DG]Abstract References Reviews Resources

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

Published 2025-05-15Version 1

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.

Comments: 21 pages

Categories: math.DG

Keywords: scalar curvature, sharp integral bound, three-dimensional complete manifold, nonnegative ricci curvature, geodesic ball

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