Weyl Law Improvement for Products of Spheres

A. Iosevich, E. Wyman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 NM(λ) = cλd+ O(λd1). 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.

Original languageEnglish (US)
Pages (from-to)593-612
Number of pages20
JournalAnalysis Mathematica
Volume47
Issue number3
DOIs
StatePublished - Sep 2021
Externally publishedYes

Keywords

  • eigenvalue
  • Laplacian
  • lattice point
  • product manifold
  • Weyl law

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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