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A lower bound for the $\Theta$ function on manifolds without conjugate points

By Yannick Bonthonneau


In this short note, we prove that the usual $\Theta$ function on a Riemannian manifold without conjugate points is uniformly bounded from below. This extends a result of Green in two dimensions. This elementary lemma implies that the B\'erard remainder in the Weyl law is valid for a manifold without conjugate points, without any restriction on the dimension

Topics: Mathematics - Differential Geometry, Mathematics - Spectral Theory
Year: 2016
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