2025/04/07 by Takao Yamaguchi, Yamaguchi, Takao, Zhilang Zhang +1
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2504.05497
openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, as a continuation of [34], we consider the Gromov-Hausdorff convergence and collapsing in the family of compact Riemannian manifolds with boundary satisfying lower bounds on the sectional curvatures of manifolds, boundaries and the second fundamental forms of boundaries, and an upper diameter bound. We describe the local geometric structure of the limit spaces, and establish some stability results including Lipschitz homotopy stability.