| Abstract: |
| In this talk, I will present some uniqueness results for the Cauchy problem for the parabolic Schrodinger equation on complete noncompact Riemannian manifolds. Under suitable assumptions on the potential $V$, we show that the integral condition required for uniqueness may be significantly weaker than in the case with no potential. The key idea is to exploit the decay of positive solutions to the corresponding stationary Schrodinger equation. |
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