Geodesic
The $\Theta$ Function and the Weyl Law on Manifolds Without Conjugate Points
Documenta mathematica, Tome 22 (2017), pp. 1275-1283
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We prove that the usual Θ function on a Riemannian manifold without conjugate points is uniformly bounded from below. This extends a result of Green in two dimensions. We deduce that the Bérard remainder in the Weyl law is valid for a manifold without conjugate points, without any restriction on the dimension.
DOI : 10.4171/dm/595
Classification : 35P20
Mots-clés : Weyl law, manifolds without conjugate points, Hadamard parametrix, Jacobi and Ricatti equations 
@article{10_4171_dm_595,
     author = {Yannick Bonthonneau},
     title = {The $\Theta$ {Function} and the {Weyl} {Law} on {Manifolds} {Without} {Conjugate} {Points}},
     journal = {Documenta mathematica},
     pages = {1275--1283},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/595},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/595/}
}
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Yannick Bonthonneau. The $\Theta$ Function and the Weyl Law on Manifolds Without Conjugate Points. Documenta mathematica, Tome 22 (2017), pp. 1275-1283. doi: 10.4171/dm/595

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