Uniformly Normal Neighborhood Lemma

Theorem

Let $\struct {M, g}$ be a Riemannian manifold.

Let $U \subseteq M$ be a neighborhood of $p \in M$.

Then there is a uniformly normal subset which is a neighborhood of $p \in M$ and is contained in $U$.

Proof

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Uniformly Normal Neighborhoods