Perturbation results concerning Gaussian estimates and hypoellipticity for left-invariant Laplacians on compact groups
Volume 172 / 2023
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.
