Given two ni-dimensional Alexandrov spaces Xi of curvature ≥ 1, the join of X1 and X2 is an (n1 + n2 + 1)-dimensional Alexandrov space X of curvature ≥ 1, which contains Xi as convex subsets such that their points are π2 apart. If a group acts isometrically on a join that preserves Xi, then the orbit space is called a 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 Xi without boundary such that X1 and X2 are at least π2 apart and dim(X1) + dim(X2) = n − 1.
All Science Journal Classification (ASJC) codes
- Applied Mathematics