\({\mathcal{PT}}\) -Symmetric Laplace–Beltrami Operator in the Strip on a Sphere

  • Petr Siegl
Open Problems


Numerical analysis indicates that all eigenvalues of a \({\mathcal{PT}}\) -symmetric Laplace–Beltrami operator in the strip on a sphere are real. However, a complete proof is not known.

Mathematics Subject Classification (2010)

58J50 35P10 81Q35 81Q12 


Laplace–Beltrami operator on a sphere \({\mathcal{PT}}\) -symmetry non-self-adjoint boundary conditions real spectrum 


  1. 1.
    Krejčiřík D., Siegl P.: \({\mathcal {PT}}\) -symmetric models in curved manifolds. J. Phys. A Math. Theor. 43(48), 485204 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Theoretical Physics, Nuclear Physics InstituteAcademy of SciencesŘežCzech Republic

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