Identification of a connection from Cauchy data on a Riemann surface with boundary

Details Identification of a connection from Cauchy data on a Riemann surface with boundary Identification of a connection from Cauchy data on a Riemann surface with boundary

2010-07-05

arxiv.org/abs/1007.0760v2

Mathematics

Differential Geometry

23 pages. Independent additional proof of Th 6.1 added. Minor typos corrected

Scientific paper

We consider a connection $\nabla^X$ on a complex line bundle over a Riemann
surface with boundary $M_0$, with connection 1-form $X$. We show that the
Cauchy data space of the connection Laplacian (also called magnetic Laplacian)
$L:={\nabla^X}^*\nabla^X + q$, with $q$ a complex valued potential, uniquely
determines the connection up to gauge isomorphism, and the potential $q$.

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