\[ \DeclareMathOperator{\Vol}{Vol} \]

Let \((M,g)\) denote a Riemannian manifold, Suppose \(\exp_p\colon B_r(0)\to U \) is a diffeomorphism on its image, then

\[ B=\exp_p (B_r(0)) \]

is called geodesic ball of radius \(r>0\) centered in \(p\in M\).

Links Link to heading

• exponential map
• \(B^d_r(p)=\exp_p (B_r(0))\)
• \(\Vol B^d_r(p) \approx \Vol B_r\)