A geometric estimate for a periodic Schrödinger operator

• Autorzy: Thomas Friedrich
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 83
• Numer: 2
• Strony: 209-216

Daty

wydano

2000

otrzymano

1999-05-14

poprawiono

1999-10-06

Twórcy

autor

Thomas Friedrich

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

Bibliografia

• [1] I. Agricola and T. Friedrich, Upper bounds for the first eigenvalue of the Dirac operator on surfaces, J. Geom. Phys. 30 (1999), 1-22.
• [2] C. Bär, Lower eigenvalues estimates for Dirac operators, Math. Ann. 293 (1992), 39-46.
• [3] T. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten Riemann- schen Mannigfaltigkeit nichtnegativer Skalarkrümmung, Math. Nachr. 97 (1980), 117-146.
• [4] T. Friedrich, Zur Abhängigkeit des Dirac-Operators von der Spin-Struktur, Colloq. Math. 48 (1984), 57-62.
• [5] T. Friedrich, On the spinor representation of surfaces in Euclidean $3$-spaces, J. Geom. Phys. 28 (1998), 143-157.
• [6] J. Lott, Eigenvalue bounds for the Dirac operator, Pacific J. Math. 125 (1986), 117-128.
• [7] U. Pinkall, Hopf tori in $S^3$, Invent. Math. 81 (1985), 379-386.
• [8] T. J. Willmore, Riemannian Geometry, Clarendon Press, Oxford, 1996.