3 problems

Let $M$ be a compact Riemannian manifold with a gradient shrinking Ricci soliton metric $g$, so that for some function $f$ and $\tau>0$, … The metric has positive curvature operato…

Let $m$ be a positive integer, and let $(M^m,g)$ be a compact Riemannian manifold with diameter $\operatorname{diam}(M)=1$. Write $\mathcal{R}m$ for its curvature operator, and let…

Nishikawa's conjecture.