Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content
Probability
2023-03-09 v2 Analysis of PDEs
Differential Geometry
Abstract
We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and study their spectral properties. We prove that these operators have a pure point spectrum, and prove the existence of the spectral gap. In addition, we give applications to the small ball problem for a hypoelliptic Brownian motion and the large time behavior of the heat content in a regular domain.
Keywords
Cite
@article{arxiv.2202.10410,
title = {Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content},
author = {Marco Carfagnini and Maria Gordina},
journal= {arXiv preprint arXiv:2202.10410},
year = {2023}
}