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arXiv · 1603.01095

Stability for a magnetic Schr\"odinger operator on a Riemann surface with boundary

Joel Andersson·Leo Tzou
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Abstract

We consider a magnetic Schr\"odinger 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 $X$.

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Joel Andersson, Leo Tzou. 2016-03-03. Stability for a magnetic Schr\"odinger operator on a Riemann surface with boundary. https://arxiv.org/abs/1603.01095

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