Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identification of a connection from Cauchy data on a Riemann surface
  with boundary   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 $q$.

26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an