Comparison theorems for the volume of a geodesic ball with a product of space forms as a model (Q1904257)

The classical theorem of Bishop and Günter gives a comparison between the volume of a geodesic ball of radius \(r\) in a Riemannian manifold of dimension \(n\) with Ricci curvature \(\rho\) bounded from below by some constant \((n- 1)k\) and the volume of a geodesic ball of radius \(r\) in a space form of sectional curvature \(k\). The authors prove two comparison theorems for the volume of a geodesic ball in a Riemannian manifold taking as a model a geodesic ball in the product of two space forms.