Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces
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Publication:1691983
DOI10.1007/s10455-017-9569-xzbMath1390.58015arXiv1701.03906OpenAlexW2578831302MaRDI QIDQ1691983
David Tewodrose, Shouhei Honda, Luigi Ambrosio
Publication date: 25 January 2018
Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.03906
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37)
Related Items (23)
Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary ⋮ Boundary regularity and stability for spaces with Ricci bounded below ⋮ 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 ⋮ On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth ⋮ Singular Weyl’s law with Ricci curvature bounded below ⋮ Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments ⋮ One dimensional 𝖱𝖢𝖣 spaces always satisfy the regular Weyl’s law ⋮ Monotonicity formulas for harmonic functions in \(\mathrm{RCD}(0,N)\) spaces ⋮ Sobolev mappings between RCD spaces and applications to harmonic maps: a heat kernel approach ⋮ Regularity of Lagrangian flows over \(\operatorname{RCD}^*(K, N)\) spaces ⋮ Subgraphs of BV functions on RCD spaces ⋮ 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 ⋮ New differential operator and noncollapsed RCD spaces ⋮ Improved regularity estimates for Lagrangian flows on \(\mathrm{RCD}(K,N)\) spaces ⋮ Collapsed Ricci limit spaces as non-collapsed RCD spaces ⋮ A note on the collapsing geometry of hyperkähler four manifolds ⋮ Stratified spaces and synthetic Ricci curvature bounds ⋮ Rigidity for positive Ricci curvature via metric measure geometry ⋮ Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces ⋮ Weakly non-collapsed RCD spaces are strongly non-collapsed
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