A geometric estimate for a periodic Schrödinger operator

Thomas Friedrich

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 2, page 209-216
  • ISSN: 0010-1354

Abstract

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

How to cite

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Friedrich, Thomas. "A geometric estimate for a periodic Schrödinger operator." Colloquium Mathematicae 83.2 (2000): 209-216. <http://eudml.org/doc/210782>.

@article{Friedrich2000,
abstract = {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.},
author = {Friedrich, Thomas},
journal = {Colloquium Mathematicae},
keywords = {spectrum; Fenchel inequality; Schrödinger operators; surfaces; Dirac operator; periodic Schrödinger operators},
language = {eng},
number = {2},
pages = {209-216},
title = {A geometric estimate for a periodic Schrödinger operator},
url = {http://eudml.org/doc/210782},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Friedrich, Thomas
TI - A geometric estimate for a periodic Schrödinger operator
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 2
SP - 209
EP - 216
AB - 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.
LA - eng
KW - spectrum; Fenchel inequality; Schrödinger operators; surfaces; Dirac operator; periodic Schrödinger operators
UR - http://eudml.org/doc/210782
ER -

References

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  1. [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. Zbl0941.58018
  2. [2] C. Bär, Lower eigenvalues estimates for Dirac operators, Math. Ann. 293 (1992), 39-46. Zbl0741.58046
  3. [3] T. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten Riemann- schen Mannigfaltigkeit nichtnegativer Skalarkrümmung, Math. Nachr. 97 (1980), 117-146. Zbl0462.53027
  4. [4] T. Friedrich, Zur Abhängigkeit des Dirac-Operators von der Spin-Struktur, Colloq. Math. 48 (1984), 57-62. Zbl0542.53026
  5. [5] T. Friedrich, On the spinor representation of surfaces in Euclidean 3 -spaces, J. Geom. Phys. 28 (1998), 143-157. Zbl0966.53042
  6. [6] J. Lott, Eigenvalue bounds for the Dirac operator, Pacific J. Math. 125 (1986), 117-128. Zbl0605.58044
  7. [7] U. Pinkall, Hopf tori in S 3 , Invent. Math. 81 (1985), 379-386. 
  8. [8] T. J. Willmore, Riemannian Geometry, Clarendon Press, Oxford, 1996. 

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