Open manifolds with uniformly positive isotropic curvature

2023/11/27 by Hong Huang, Huang, Hong
Mathematics · #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2311.15825

openalex publication_date 2023/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the following result: Let (M,g₀) be a complete noncompact manifold of dimension n≥ 12 with isotropic curvature bounded below by a positive constant, with scalar curvature bounded above, and with injectivity radius bounded below. Then there is a finite collection X of spherical n-manifolds and manifolds of the form \mathbbS^n-1 × ℝ /G, where G is a discrete subgroup of the isometry group of the round cylinder \mathbbS^n-1× ℝ, such that M is diffeomorphic to a (possible infinite) connected sum of members of X. This extends a recent work of Huang. The proof uses Ricci flow with surgery on open orbifolds with isolated singularities.

Related

• Classification of compact manifolds with positive isotropic curvature
• Compact manifolds of dimension n≥ 12 with positive isotropic curvature
• Complete 4-manifolds with uniformly positive isotropic curvature
• Manifolds with positive isotropic curvature of dimension at least nine
• On the topology of manifolds with positive isotropic curvature