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

Volume 172 / 2023

Qi Hou, Laurent Saloff-Coste Colloquium Mathematicum 172 (2023), 105-128 MSC: Primary 22E66; Secondary 31C25, 60G51, 60B15. DOI: 10.4064/cm8696-8-2022 Published online: 8 November 2022

Abstract

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.

Authors

  • Qi HouYanqi Lake Beijing Institute of
    Mathematical Sciences and Applications
    Yanqihu, Huairou District
    Beijing, China
    e-mail
    e-mail
  • Laurent Saloff-CosteDepartment of Mathematics
    Cornell University
    567 Malott Hall
    Ithaca, New York, United States
    e-mail

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