Abstract
The classical Weyl Law says that if NM(λ) denotes the number of eigenvalues of the Laplace operator on a d-dimensional compact manifold M without a boundary that are less than or equal to λ, then
This paper explores the prospects of improvements of Weyl remainders on products of manifolds. In particular we obtain a polynomial improvement to the Weyl remainder for products of spheres, demonstrate how Duistermaat and Giullemin’s result implies a little-o improvement to the remainder for products of compact Riemannian manifolds without boundary, and conjecture that polynomial improvements hold for these more general products.
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The work of the first listed author was supported in part by the National Science Foundation under grant no. HDR TRIPODS-1934962.
The work of the second listed author was supported in part by the National Science Foundation under grant no. DMS-1502632.
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Iosevich, A., Wyman, E. Weyl Law Improvement for Products of Spheres. Anal Math 47, 593–612 (2021). https://doi.org/10.1007/s10476-021-0090-x
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DOI: https://doi.org/10.1007/s10476-021-0090-x