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Lp Convergence of AMV Laplacians on completions of Riemannian manifolds
Abstract
We study conditions for the Lp convergence of the AMV Laplacian Δr on completions of Riemannian manifolds (M,g). The condition invloves the Minkowski dimension of the set M̅ ∖ 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
@misc{dias2026convergence,
title = {{$L^p$ Convergence of AMV Laplacians on completions of Riemannian manifolds}},
author = {Manuel Dias},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36125},
eprint = {2610.36125},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36125},
}
RIS
TY - UNPB
TI - L^p Convergence of AMV Laplacians on completions of Riemannian manifolds
AU - Manuel Dias
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36125
UR - https://arxiv.org/abs/2610.36125
AB - 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 M̅ ∖ 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.
ER -