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

Ovidiu Munteanu; Jiaping Wang

doi:10.48550/arxiv.2505.10520

May 15, 2025Open Access

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

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Key Points

The integral of scalar curvature is bounded above by 8πR asymptotically for large R.
Bounds are established under the condition of nonnegative Ricci curvature.
The scalar curvature must remain between two positive constants for these results to hold.
This work contributes to understanding geometric properties in 3-manifolds with specific curvature conditions.

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Implication

This analysis reveals integral bounds on scalar curvature in 3-manifolds, suggesting limits influenced by Ricci curvature.

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 8π R asymptotically for large R provided that the scalar curvature is bounded between two positive constants.

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Cite This Study

Munteanu et al. (2025) studied this question.

synapsesocial.com/papers/68f163c79903599108abcba8 https://doi.org/10.48550/arxiv.2505.10520

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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