2 problems

Let $M$ be a manifold and let $\operatorname{Prob}(M)$ denote the space of probability densities on $M$. For $p\in(1,\infty)$, consider the geodesic equation of the $L^p$-Fisher--R…

Let $r$ denote the Sobolev order of the homogeneous metric, and consider smooth mean-zero solutions associated with this metric. Critical regularity conjecture. There is a critical…