$L^p$ Convergence of AMV Laplacians on completions of Riemannian manifolds

Abstract

We study conditions for the $L^p$ convergence of the AMV Laplacian ${\Delta }_r$ on completions of Riemannian manifolds $(M,g)$. The condition invloves the Minkowski dimension of the set $\overline{M}\setminus M$ and how much the curvature is blowing up around $S$. We build a concrete family of sets that satisfies these conditions, and provide an example of non convergence when these conditions are not met.

arXiv comment54 pages