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

A W1,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 gk converges in W1,p to a limit metric g, then the corresponding distance functions dgk subconverge to a limit distance function d, which satisfies d ≤ dg. As an application, we show that the above convergence result applies to a sequence of conformal metrics with L^n/2--bounded scalar curvatures, under certain geometric assumptions. In particular, in this special setting, the limit distance function d actually coincides with dg.

Duke Scholars

Author Conghan Dong Mathematics