Spectral properties of symmetrized AMV operators

Manuel Dias; David Tewodrose

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arXiv · 2411.10202

Spectral properties of symmetrized AMV operators

Manuel Dias·David Tewodrose

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Abstract

The symmetrized Asymptotic Mean Value Laplacian $\tildeΔ$, obtained as limit of approximating operators $\tildeΔ_r$, is an extension of the classical Euclidean Laplace operator to the realm of metric measure spaces. We show that, as $r \downarrow 0$, the operators $\tildeΔ_r$ eventually admit isolated eigenvalues defined via min-max procedure on any compact locally Ahlfors regular metric measure space. Then we prove $L^2$ and spectral convergence of $\tildeΔ_r$ to the Laplace--Beltrami operator of a compact Riemannian manifold, imposing Neumann conditions when the manifold has a non-empty boundary.

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BibTeX RIS

Manuel Dias, David Tewodrose. 2025-08-06. Spectral properties of symmetrized AMV operators. https://arxiv.org/abs/2411.10202

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