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

Manuel Dias

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arXiv · 2610.36125

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

Manuel Dias

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Abstract

We study conditions for the $L^p$ convergence of the AMV Laplacian $Δ_r$ 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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BibTeX RIS

Manuel Dias. 2026-10-26. $L^p$ Convergence of AMV Laplacians on completions of Riemannian manifolds. https://arxiv.org/abs/2610.36125

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