Published 2010
| Submitted
Journal Article
Open
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group
- Creators
-
Frank, Rupert L.
- Laptev, Ari
Abstract
We prove that for any domain in the Heisenberg group the (k+1)'th Neumann eigenvalue of the sub-Laplacian is strictly less than the k'th Dirichlet eigenvalue. As a byproduct we obtain similar inequalities for the Euclidean Laplacian with a homogeneous magnetic field.
Additional Information
© The Author 2010. Published by Oxford University Press. Received June 8, 2009; Accepted December 2, 2009 Communicated by Prof. Peter Sarnak The authors acknowledge interesting discussions with A. Hansson concerning the topics of this paper. The first author wishes to thank E. Lieb and R. Seiringer for helpful remarks. Support through DFG grant FR 2664/1-1 and U.S. NSF grant PHY 06 52854 (R.F.) is gratefully acknowledged. Recently, Bernard Helffer suggested a way of proving similar estimates for a large class of sub-elliptic operators. This will be the subject of a forthcoming publication.Attached Files
Submitted - 0906.1402.pdf
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0906.1402.pdf
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Additional details
- Eprint ID
- 77801
- Resolver ID
- CaltechAUTHORS:20170526-092032067
- FR 2664/1-1
- Deutsche Forschungsgemeinschaft (DFG)
- PHY-0652854
- NSF
- Created
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2017-05-26Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field