Finite Quotient of Join in Alexandrov Geometry

2016/09/25 by Xiaochun Rong, Rong, Xiaochun, Yusheng Wang +1 · 1 citation
Mathematics · #51F99 #53C20 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1609.07747

openalex publication_date 2016/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given two n_i-dimensional Alexandrov spaces X_i of curvature ≥ 1, the join of X₁ and X₂ is an (n₁+n₂+1)-dimensional Alexandrov space X of curvature ≥ 1, which contains X_i as convex subsets such that their points are \frac π2 apart. If a group acts isometrically on a join that preserves X_i, then the orbit space is called quotient of join. We show that an n-dimensional Alexandrov space X with curvature ≥ 1 is isometric to a finite quotient of join, if X contains two compact convex subsets X_i without boundary such that X₁ and X₂ are at least \frac π2 apart and dim(X₁)+dim(X₂)=n-1.

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• Rigidity for positively curved Alexandrov spaces with boundary

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