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A Lichnerowicz estimate for the spectral gap of a sub-Laplacian


Authors: Stine Marie Berge and Erlend Grong
Journal: Proc. Amer. Math. Soc. 147 (2019), 5153-5166
MSC (2010): Primary 47A75, 35H20, 53C17
DOI: https://doi.org/10.1090/proc/14223
Published electronically: September 20, 2019
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Abstract: For a second order operator on a compact manifold satisfying the strong Hörmander condition, we give a bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian of a Riemannian manifold. We consider a wide class of such operators which includes horizontal lifts of the Laplacian on Riemannian submersions with minimal leaves.


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Additional Information

Stine Marie Berge
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: stine.m.berge@ntnu.no

Erlend Grong
Affiliation: Université Paris Sud, Laboratoire des Signaux et Systèmes (L2S) Supélec, CNRS, Université Paris-Saclay, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France; and Department of Mathematics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway
Email: erlend.grong@gmail.com

DOI: https://doi.org/10.1090/proc/14223
Keywords: Spectral gap, Lichnerowicz estimate, sub-Laplacian
Received by editor(s): August 18, 2017
Published electronically: September 20, 2019
Additional Notes: The second author was supported by the Research Council of Norway (project number 249980/F20). The authors were partially supported by the joint NFR-DAAD project 267630/F10. Results are partially based on the first author’s Master Thesis at the University of Bergen, Norway.
Communicated by: Lei Ni
Article copyright: © Copyright 2019 American Mathematical Society