3 problems

Milman's contraction conjecture. There exists a map

Uniform curvature bound conjecture. The curvature remains uniformly bounded up to the maximal time:

Let $(M,g)$ be an asymptotically hyperbolic $3$-manifold with scalar curvature $R\geq -6$ and mass $M$. Let $\Sigma_0$ be an outermost sphere with mean curvature $H(\Sigma_0)=2$. W…