A geometric estimate for a periodic Schr\"odinger operator whose potential is the curvature of a spherical curve

Thomas Friedrich

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classification 🧮 math.DG

keywords curvaturecurveestimategeometricoperatorperiodicpotentialbelow

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We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator $- 4 d^2/ds^2 + \kappa^2 (s)$ with potential given by the curvature of a closed curve.

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A geometric estimate for a periodic Schr\"odinger operator whose potential is the curvature of a spherical curve

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