Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content

Marco Carfagnini; Maria Gordina

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arXiv · 2202.10410

Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content

Marco Carfagnini·Maria Gordina

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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.

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BibTeX RIS

Marco Carfagnini, Maria Gordina. 2022-02-21. Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content. https://arxiv.org/abs/2202.10410

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