Accepted Paper
Inserted: 13 nov 2025
Last Updated: 13 nov 2025
Journal: Journal of Spectral Theory
Year: 2025
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.