The \(\Theta\) function and the Weyl law on manifolds without conjugate points (Q1677389)
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scientific article; zbMATH DE number 6810412
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(\Theta\) function and the Weyl law on manifolds without conjugate points |
scientific article; zbMATH DE number 6810412 |
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The \(\Theta\) function and the Weyl law on manifolds without conjugate points (English)
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21 November 2017
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This paper proves that on a Riemannian manifold without conjugate points, the Theta function is uniformly bounded from below. This result is used to obtain a Weyl-type asymptotic formula for the eigenvalue counting function, extending a result which has previously been proven by \textit{P. H. Bérard} [Math. Z. 155, 249--276 (1977; Zbl 0341.35052)] for manifolds of dimension two to manifolds of arbitrary dimension without conjugate points.
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Weyl law
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manifolds without conjugate points
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Hadamard parametrix
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Jacobi and Riccati equations
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