Rigidity of Area-Minimizing 2-Spheres in n-Manifolds with Positive Scalar Curvature

2019/03/14 by Jintian Zhu, Zhu, Jintian · 4 citations
Mathematics · #53C24 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:53C24 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1903.05785

11 pages, fix a gap in section 3 in previous version

openalex publication_date 2019/03/14 · arxiv created 2019/03/28 · arxiv updated 2019/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the least area of the non-contractible immersed spheres is no more than 4π in any oriented compact manifold with dimension n+2≤ 7 which satisfies R≥ 2 and admits a map to \mathbf S²× Tⁿ with nonzero degree. We also prove a rigidity result for the equality case. This can be viewed as a generalization of the result in [2] to higher dimensions.

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