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arXiv · 2110.07481

Perturbation results concerning Gaussian estimates and hypoellipticity for left-invariant Laplacians on compact groups

Qi Hou·Laurent Saloff-Coste
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Abstract

In this paper we study left-invariant Laplacians on compact connected groups that are form-comparable perturbations of bi-invariant Laplacians. Our results show that Gaussian bounds for derivatives of heat kernels enjoyed by certain bi-invariant Laplacians hold for their form-comparable perturbations. We further show that the parabolic operators associated with such left-invariant Laplacians, in particular, with the bi-invariant Laplacians, are hypoelliptic in various senses.

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Qi Hou, Laurent Saloff-Coste. 2021-10-14. Perturbation results concerning Gaussian estimates and hypoellipticity for left-invariant Laplacians on compact groups. https://arxiv.org/abs/2110.07481

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