##  [Convexity Radius](/convexity-radius) 

  ##  [Convexity Radius](https://puremath.quantumdictionary.io/convexity-radius-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

At a point p of a Riemannian manifold, the convexity radius is the largest r>0 such that the geodesic ball B(p,r) is (strongly) geodesically convex: any two points in B(p,r) are joined by a unique minimizing geodesic lying entirely in B(p,r).