The strengthened Gromov positive simplicial volume conjecture

Let $M$ be a closed, connected, oriented topological $n$-manifold. Suppose that $M$ admits a Riemannian metric whose sectional curvature is nonpositive everywhere and whose Ricci curvature is negative definite at a point. Strengthened Gromov positive simplicial volume conjecture. Then

$$||M||>0.$$

This is a strengthening of the conjecture requiring negative definite Ricci curvature everywhere. The source attributes this stronger formulation to work cited as CW20 and notes partial results for locally symmetric spaces and rank-one manifolds with stronger Ricci hypotheses; the conjecture remains open.