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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