The Grushin hemisphere as a Ricci limit space with curvature ≥ 1

2022/11/04 by Jiayin Pan, Pan, Jiayin · 1 citation
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2211.02747

openalex publication_date 2022/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere S^m+n with Ric≥ 1 such that its Gromov-Hausdorff limit is the n-dimensional Grushin hemisphere.

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