A Myers theorem via m-Bakry-Émery curvature

Abstract

In this paper, we prove that a complete manifold whose m-Bakry-Émery curvature satisfies
Ric_f,m(x) ≥ −(m − 1) $\frac{K_0}{(1+r(x))^2}$
for some constant K₀ < $-\frac{1}{4}$ should be compact. We also get an upper bound estimate for the diameter.