A Compactness Theorem for Riemannian Manifolds with Boundary and Applications

Kenneth S. Knox

In this paper, we prove $W^{1,p}$ ($p>n$) and $C^{0,\alpha }$ ($0<\alpha <1$) precompactness for classes of Riemannian $n$-manifolds with boundary satisfying uniform $L^{\infty }$ bounds on…