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We investigate nodal sets of magnetic Schroedinger operators with zeromagnetic field, acting on a non simply connected domain in $\r^2$. For the caseof circulation 1/2 of the magnetic vector potential around each hole in theregion, we obtain a charactisation of the nodal set, and use this to obtainbounds on the multiplicity of the groundstate. For the case of one hole and afixed electric potential, we show that the first eigenvalue takes its highestvalue for circulation 1/2.Comment: 30 pages, 8 figure

Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains