$W^{1,p}$-metrics and conformal metrics with $L^{n/2}$-bounded scalar curvature

Conghan Dong, Yuxiang Li, Ke Xu

A $W^{1,p}$-metric on an $n$-dimensional closed Riemannian manifold naturally induces a distance function, provided $p$ is sufficiently close to $n$. If a sequence of metrics $g_k$…