Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds
<p dir="ltr">We prove eigenvalue bounds for Schrödinger operator −∆<sub>g</sub> + V on compact manifolds with complex potentials V . The bounds depend only on an L<sup>q</sup> -norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank’s [9] results in the Euclidean case.</p>
Funding
EPSRC New Investigator Award (J. Cuenin) : EP/X011488/1
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Forum MathematicumPublisher
De GruyterVersion
- AM (Accepted Manuscript)
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© Walter de Gruyter GmbH, Berlin/BostonPublisher statement
This is an Accepted Manuscript of an article published by De Gruyter in on Forum Mathematicum, available at Ehttps://doi.org/10.1515/forum-2024-0564 It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. If you wish to use this manuscript for commercial purposes, please contact rights@degruyter.com.Acceptance date
2025-07-21Publication date
2025-08-01Copyright date
2025ISSN
0933-7741eISSN
1435-5337Publisher version
Language
- en
