Radius of locally convex subsets in Alexandrov spaces with curvature≥1 and radius>π/2

Abstract

Let X be a complete Alexandrov space with curvature≥1 and radius>π/2. We prove that any connected, complete, and locally convex subset without boundary in X also has the radius>π/2.

Keywords

Alexandrov space / convex subset / radius

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Higher Education Press and Springer-Verlag Berlin Heidelberg