A geometric estimate for a periodic Schrödinger operator whose potential is the curvature of a spherical curve

1999/04/22 by Thomas Friedrich, Friedrich, Thomas
Computer Science · Mathematics · #53A05 #58G25 #Advanced Mathematical Modeling in Engineering #Curvature #Differential Geometry (math.DG) #Eigenvalues and eigenvectors #FOS: Mathematics #Geometry #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Operator (biology) #Physics #Quantum mechanics #Schrödinger's cat #Spectral Theory in Mathematical Physics #math.DG #msc:53A05 #msc:58G25

paper · pdf · doi:10.48550/arxiv.math/9904123

Latex2.09, 9 pages

openalex publication_date 1999/04/22 · arxiv created 1999/04/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator - 4 d²/ds² + κ² (s) with potential given by the curvature of a closed curve.

Citations

• Hopf tori inS 3
• Upper bounds for the first eigenvalue of the Dirac operator on surfaces

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