A geometric estimate for a periodic Schrödinger operator

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Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, D-10099 Berlin, Germany

We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator

- 4 \frac{d^{2}}{d s^{2}} + κ^{2} (s)

with potential given by the curvature of a closed curve.

spectrum, Fenchel inequality, Schrödinger operators, surfaces, Dirac operator

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