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Potential Analysis

, Volume 50, Issue 4, pp 621–630 | Cite as

The Lowest Eigenvalue of Schrödinger Operators on Compact Manifolds

  • Michael G. DabkowskiEmail author
  • Michael T. Lock
Article
  • 37 Downloads

Abstract

The lowest eigenvalue of the Schrödinger operator \(-{\Delta }+\mathcal {V}\) on a compact Riemannian manifold without boundary is studied. We focus on the particularly subtle case of a sign changing potential with positive average.

Keywords

Schrödinger equation Spectral problems Riemannian geometry 

Mathematics Subject Classification (2010)

53C21 58J05 35J10 35P15 

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Notes

Acknowledgements

The authors would like to thank Joseph Conlon and Pablo Stinga for many useful conversations, as well as Herschel Viminah and Avram Mahnool for their insight into the physical aspects of this problem. The authors are also grateful to the referee for careful consideration and valuable suggestions.

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Authors and Affiliations

  1. 1.Department of MathematicsLawrence Technological UniversitySouthfieldUSA
  2. 2.Department of MathematicsUniversity of TexasAustinUSA

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