A comparison of the eigenvalues of the Dirac and Laplace operators on a two-dimensional torus

Manuscripta Mathematica

Volumn 100, Issue 2, 1999, Pages 231-258

  Agricola, Ilka ^a   Ammann, Bernd ^a   Friedrich, Thomas ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033472428     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002290050239     Document Type: Article

References (10)

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2. Ammann, B.: Spin-Strukturen und das Spektrum des Dirac-Operators. Dissertation Freiburg 1998, Shaker-Verlag Aachen, 1998
3. Bär, Chr.: Lower eigenvalues estimates for Dirac operators. Math. Ann. 293, 39-46 (1992)
4. Friedrich, Th.: Dirac-Operatoren in der Riemannschen Geometrie. Braunschweig/Wiesbaden: Vieweg-Verlag, 1997
5. Hartman, P.: Ordinary differential equations. New York: 1964
6. Hijazi, O.: A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Commun. Math. Phys. 104, 151-162 (1986)
7. Li, P., Yau,: A new conformal invariant and its application to the Willmore conjecture and the first eigenvalue of compact surfaces. Invent. Math. 69, 269-291 (1982)
8. Lott, J.: Eigenvalue bounds for the Dirac operator. Pac. Journ. Math. 125, 117-128 (1986)
9. Reed, M., Simon, B.: Methods of modern mathematical physics, Part IV. Boston: Academic Press, 1978
10. Whittaker, E.T., Watson, G.N.: A course of modern analysis. Cambridge: Cambridge University Press, 1927