The Nonlinear Schr¨odinger Equation on the Hyperbolic Space

@inproceedings{Banica2005TheNS,
  title={The Nonlinear Schr¨odinger Equation on the Hyperbolic Space},
  author={Valeria Banica},
  year={2005}
}
In this article we study some aspects of dispersive and concentration phenomena for the Schrödinger equation posed on the hyperbolic space H n , in order to see if the negative curvature of the manifold gets the dynamics stabler than in the Euclidean case. It is indeed the case : we prove that the dispersion inequality is valid, in a stronger form than the one on R n. However, the geometry is not enough influent to avoid the concentration phenomena. We prove that the critical nonlinearity power… CONTINUE READING

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