Effective volume growth of three-manifolds with positive scalar curvature

2024/05/05 by Wang, Yipeng
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2405.03023

Abstract

In this note, we prove an effective linear volume growth for complete three-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. This recovers the results obtained by Munteanu-Wang. Our method builds upon recent work by Chodosh-Li-Stryker, which utilizes the technique of μ-bubbles and the almost-splitting theorem by Cheeger-Colding.

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• Volume growth of 3-manifolds with scalar curvature lower bounds
• Geometry of three-dimensional manifolds with positive scalar curvature
• Geometry of positive scalar curvature on complete manifold
• Optimal asymptotic volume ratio for noncompact 3-manifolds with asymptotically nonnegative Ricci curvature and a uniformly positive scalar curvature lower bound
• Volume growth functions of complete Riemannian manifolds with positive scalar curvature