Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature

2026/07/27 by Jiangcheng You, Heng Zhang
#math.DG

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Abstract

We prove that a contractible 3-manifold admitting a complete Riemannian metric of nonnegative scalar curvature is diffeomorphic to \R³. We also prove that, if the interior M_γ of a compact handlebody of genus γ admits such a metric, then γ≤1. This answers two open questions posed by Wang and Gromov, respectively.

Citations

• 3-Manifolds with positive scalar curvature and bounded geometry
• Gradient estimates for scalar curvature
• Noncompact Fill-Ins of Bartnik Data
• Four Lectures on Scalar Curvature
• Contractible 3-manifold and Positive scalar curvature (II)
• Contractible 3-manifold and Positive scalar curvature (I)
• Comparison results for capacity
• Smooth Approximation of Lipschitz functions on Riemannian manifolds
• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

Related

• Topological Rigidity and Positive scalar curvature
• 3-Manifolds with positive scalar curvature and bounded geometry
• Contractible 3-manifold and Positive scalar curvature (II)
• Contractible 3-manifold and Positive scalar curvature (I)
• Rigidity of area minimizing tori in 3-manifolds of nonnegative scalar curvature