Contractible 3-manifold and Positive scalar curvature (I)

2019/01/14 by Jian Wang, Wang, Jian · 2 citations
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1901.04605

openalex publication_date 2019/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we prove that the Whitehead manifold has no complete metric of positive scalar curvature. This result can be generalized to the genus one case. Precisely, we show that no contractible genus one 3-manifold admits a complete metric of positive scalar curvature.

Citations

• Limit leaves of a CMC lamination are stable
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds
• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

Cited by

• Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature
• Positive curvature conditions on contractible manifolds

Related

• Contractible 3-manifold and Positive scalar curvature (II)
• 3-Manifolds with positive scalar curvature and bounded geometry
• Topological Rigidity and Positive scalar curvature
• Equivariant 3-manifolds with positive scalar curvature
• Scalar Curvature on some Open 3-Manifolds