##  [Injectivity Radius](/injectivity-radius) 

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

  

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Definition

At a point p in a Riemannian manifold, the largest radius r>0 such that the exponential map exp_p restricts to a diffeomorphism from the open ball of radius r in T_pM onto its image in M; globally one may take the infimum over p for a manifold injectivity radius.