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This research aims to derive geometric properties related to volume in three-dimensional manifolds with positive scalar curvature.

Geometry of three-dimensional manifolds with positive scalar curvature

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Research demonstrates volume growth in three-dimensional manifolds with positive scalar curvature, suggesting new geometric insights.

This research aims to derive geometric properties related to volume in three-dimensional manifolds with positive scalar curvature.
Derived volume estimates for complete three-dimensional manifolds with positive scalar curvature.
Analyzed cases where Ricci curvature is nonnegative and scalar curvature is bounded from below.
Explored volume growth when scalar curvature decays towards zero.
Proved that volume of the manifold shows linear growth when scalar curvature is positively bounded.
Confirmed Gromov's question regarding volume growth for three-dimensional manifolds positively.
Established similar results for cases with asymptotically nonnegative Ricci curvature.

Munteanu et al. (2026) studied this question.

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