Convexity radius

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Template:Radius notion

Definition

Definition with symbols

Let p be a point in a Riemannian manifold (M,g). Then, the convexity radius at p is defined as the supremum of all radii r for which the following two conditions hold:

  • Any metric ball contained in the metric ball B_r(p) is strongly convex
  • Any geodesic segment contained in B_r(p) is a minimal geodesic joining its endpoints