# Laplace–Beltrami operators on noncommutative tori

@article{Ha2019LaplaceBeltramiOO,
title={Laplace–Beltrami operators on noncommutative tori},
author={Hyunsu Ha and Raphael Ponge},
journal={Journal of Geometry and Physics},
year={2019}
}
• Published 22 May 2019
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• Journal of Geometry and Physics
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This paper is the first part of a two-paper series whose aim is to give a thorough account on Connes’ pseudodifferential calculus on noncommutative tori. This pseudodifferential calculus has been
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This paper is the second part of a two-paper series whose aim is to give a detailed description of Connes’ pseudodifferential calculus on noncommutative [Formula: see text]-tori, [Formula: see text].
As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the