Bishop–Gromov inequality
= Bishop–Gromov inequality
{wiki=Bishop–Gromov_inequality}
The Bishop–Gromov inequality is a fundamental result in Riemannian geometry that provides a comparison between the volume of geodesic balls in a Riemannian manifold and the volume of balls in a model space of constant curvature, specifically spherical or Euclidean spaces. The inequality is particularly useful in the context of manifolds with bounded sectional curvature.