sentences:  Let ("M", "g") be a compact "m"-dimensional Riemannian manifold with injectivity radius inj("M").Let "vol" denote the volume form on "M" and let "c""m"("r") denote the volume of the standard "m"-dimensional sphere of radius "r".Then
  
  with equality if and only if ("M", "g") is isometric to the "m"-sphere S"m" with its usual round metric.