Weyl's law on \(RCD^{\ast} (K, N)\) metric measure spaces

DOI10.4310/CAG.2019.v27.n8.a8zbMath1464.53052arXiv1701.01967WikidataQ126314793 ScholiaQ126314793MaRDI QIDQ2289774

Xi-Ping Zhu, Hui-Chun Zhang

Publication date: 24 January 2020

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.01967

zbMATH Keywords

asymptotic formulaDirichlet eigenvaluegeneralized Ricci curvature

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (14)

Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary ⋮ Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below ⋮ Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions ⋮ Singular Weyl’s law with Ricci curvature bounded below ⋮ First-order heat content asymptotics on \(\mathsf{RCD} (K, N)\) spaces ⋮ One dimensional 𝖱𝖢𝖣 spaces always satisfy the regular Weyl’s law ⋮ Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces ⋮ Spectral convergence of high-dimensional spheres to Gaussian spaces ⋮ Unique continuation problem on RCD spaces. I ⋮ On the notion of Laplacian bounds on 𝑅𝐶𝐷 spaces and applications ⋮ Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature ⋮ Isometric immersions of \(\mathrm{RCD}(K, N)\) spaces via heat kernels ⋮ A weak Weyl's law on compact metric measure spaces ⋮ Collapsed Ricci limit spaces as non-collapsed RCD spaces

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