Calabi-Yau type theorem for complete manifolds with nonnegative scalar curvature

2024/02/23 by Jintian Zhu, Zhu, Jintian · 1 citation
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.2402.15118

openalex publication_date 2024/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are able to prove an analogy of the Calabi-Yau theorem for complete Riemannian manifolds with nonnegative scalar curvature which are aspherical at infinity. The key tool is an existence result for arbitrarily large bounded regions with weakly mean-concave boundary in Riemannian manifolds with sublinear volume growth. As an application, we use the same tool to show that a complete contractible Riemannian 3-manifold with positive scalar curvature and sublinear volume growth is necessarily homeomorphic to \mathbb R³.

Cited by

• Area-charge inequalities and rigidity of time-symmetric initial data sets

Related

• 3-Manifolds with positive scalar curvature and bounded geometry
• The modified Calabi-Yau problems for CR-manifolds and applications
• Geometry of positive scalar curvature on complete manifold
• Geometry of three-dimensional manifolds with positive scalar curvature
• Contractible 3-manifold and Positive scalar curvature (II)