Riesz means of the counting function of the Laplace operator on compact manifolds of non-positive curvature

Kamil Mroz; Alexander Strohmaier

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arXiv · 1409.1869

Riesz means of the counting function of the Laplace operator on compact manifolds of non-positive curvature

Kamil Mroz·Alexander Strohmaier

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Abstract

Let $(M, {g})$ be a compact, $d$-dimensional Riemannian manifold without boundary. Suppose further that $(M,g)$ is either two dimensional and has no conjugate points or $(M,g)$ has non-positive sectional curvature. The goal of this note is to show that the long time parametrix obtained for such manifolds by B\'erard can be used to prove a logarithmic improvement for the remainder term of the Riesz means of the counting function of the Laplace operator.

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BibTeX RIS

Kamil Mroz, Alexander Strohmaier. 2014-09-05. Riesz means of the counting function of the Laplace operator on compact manifolds of non-positive curvature. https://arxiv.org/abs/1409.1869

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