In $1969$, Margulis proved, for suitable constant $r,h>0$ that :

$a(p)=\lim_{r\to \infty} \frac{VolS(p,r)}{e^{h r}}$ with ($(S(p,r)$ is geodesic spheres),exists and applied for manifolds with negative curvature which it is the main result implies purely exponential growth of volume of geodesic spheres.Really I'am curiouse to know if this limit does exist for Manifolds with positive curvature ,we may lookk to apply this in unit tangent bundle of $S^4$ ? and what about continuity of $a(p)$ in this case ?