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Dirichlet Sub-Laplacians on Homogeneous Carnot Groups: Spectral Properties, Asymptotics, and Heat Content
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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- Award ID(s):
- 1954264
- PAR ID:
- 10496724
- Publisher / Repository:
- Oxford Academic
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2024
- Issue:
- 3
- ISSN:
- 1073-7928
- Page Range / eLocation ID:
- 1894 to 1930
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imrn/rnad065
