Rellich-Kondrakov embedding of the Laplacian resolvent on the torus

Abstract

This paper proves that the domain of the Laplacian, $\DEL,$ on a closed Riemannian manifold, $(M,g),$ is compactly embedded in $L^2(M).$ Particularly, the resolvent of the Laplacian, $(\DEL + 1)^{-1},$ is shown to be compactly embedded on the torus.

10 pages