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Stability for a magnetic Schrödinger operator on a Riemann surface with boundary

The second author is supported by ARC Future Fellowship FT-130101346, the first author was employed by Vetenskapsrådet Project VR 170630

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  • We consider a magnetic Schrödinger operator $(\nabla^X)^*\nabla^X+q$ on a compact Riemann surface with boundary and prove a $\log\log$-type stability estimate in terms of Cauchy data for the electric potential and magnetic field under the assumption that they satisfy appropriate a priori bounds. We also give a similar stability result for the holonomy of the connection 1-form $X$.

    Mathematics Subject Classification: Primary: 35, 51; Secondary: 58.


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