sentences:  Berger–Kazdan comparison theorem
  
  In mathematics, the Berger–Kazdan comparison theorem is a result in Riemannian geometry that gives a lower bound on the volume of a Riemannian manifold and also gives a necessary and sufficient condition for the manifold to be isometric to the "m"-dimensional sphere with its usual "round" metric.The theorem is named after the mathematicians Marcel Berger and Jerry Kazdan.