A Smooth Intrinsic Flat Limit of with Negative Curvature

2024/06/21 by Jared Krandel, Krandel, Jared, Paul Sweeney +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2406.15332

openalex publication_date 2024/06/21 · openalex created_date 2024/06/25 · openalex updated_date 2026/07/30

Abstract

In 2014, Gromov asked if nonnegative scalar curvature is preserved under intrinsic flat convergence. Here we construct a sequence of closed oriented Riemannian n-manifolds, n≥ 3, with positive scalar curvature such that their intrinsic flat limit is a Riemannian manifold with negative scalar curvature.

Related

• Intrinsic flat convergence with bounded Ricci curvature
• Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature
• More Extreme Limits of Manifolds with Positive Scalar Curvature
• Intrinsic flat and Gromov-Hausdorff convergence of manifolds with Ricci\n curvature bounded below
• Metric limits of manifolds with positive scalar curvature