3-Manifolds with positive scalar curvature and bounded geometry

2025/02/13 by Otis Chodosh, Chodosh, Otis, Yi Lai +3 · 5 citations
Mathematics · #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2502.09727

openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be \mathbb R³. We also show that an open handlebody of genus larger than 1 does not admit complete metrics with positive scalar curvature and bounded geometry. Our results rely on the maximal weak solution to inverse mean curvature flow due to the third-named author.

Cited by

• Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature
• Proper solutions of the 1/H-flow and the Green kernel of the p-Laplacian
• Minimal surfaces and comparison geometry
• Stability of weighted minimal hypersurfaces under a lower 1-weighted Ricci curvature bound
• Positive curvature conditions on contractible manifolds

Related

• Contractible 3-manifold and Positive scalar curvature (I)
• Contractible 3-manifold and Positive scalar curvature (II)
• Topology of 3-manifolds with uniformly positive scalar curvature
• Three-manifolds with bounded curvature and uniformly positive scalar curvature
• Topological Rigidity and Positive scalar curvature