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

arXiv:2610.36125v1 Announce Type: new 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.

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