Weyl's law for singular Riemannian manifolds

Abstract : We study the asymptotic growth of the eigenvalues of the Laplace-Beltrami operator on singular Riemannian manifolds, where all geometrical invariants appearing in classical spectral asymptotics are unbounded, and the total volume can be infinite. Under suitable assumptions, we prove that the leading term of the Weyl's asymptotics contains information on the singularity, i.e. its Minkowski dimension and its regularized measure. We apply our results to a particular class of almost-Riemannian structures. A key tool in the proof is a universal estimate for the remainder of the heat trace on Riemannian manifolds, which is of independent interest.
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https://hal.archives-ouvertes.fr/hal-01902740
Contributeur : Dario Prandi <>
Soumis le : mardi 23 octobre 2018 - 17:34:34
Dernière modification le : samedi 10 novembre 2018 - 01:11:42

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ChitourPrandiRizzi.pdf
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  • HAL Id : hal-01902740, version 1

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Yacine Chitour, Dario Prandi, Luca Rizzi. Weyl's law for singular Riemannian manifolds. IF_PREPUB. 2018. 〈hal-01902740〉

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