Optimal volume bound and volume growth for manifolds with nonnegative Ricci curvature and positive bi-Ricci curvature

In this talk, we will first review Gromov’s volume bound conjecture and its variant,
the volume growth conjecture, for manifolds with nonnegative Ricci curvature and
positive scalar curvature. As natural generalisations we show how to prove
analogies of these conjecture for with nonnegative Ricci curvature and positive bi-
Ricci curvature when the dimension is less than eight. This is a joint work with
Prof. Jie Zhou from Capital Normal University.