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Volumn 240, Issue 2, 2002, Pages 423-449

Dirac eigenvalue estimates on surfaces

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EID: 0036628213     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002090100392     Document Type: Article
Times cited : (12)

References (48)
  • 1
    • 0013308216 scopus 로고    scopus 로고
    • Preprint April, Hamburger Beiträge zur Mathematik, no. 95
    • B. Ammann, Spectral estimates on 2-tori, Preprint April 2000, Hamburger Beiträge zur Mathematik, no. 95
    • (2000) Spectral Estimates on 2-Tori
    • Ammann, B.1
  • 4
    • 0002171129 scopus 로고
    • The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces
    • C. Bär, The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces, Arch. Math. 59 (1992), 65-79
    • (1992) Arch. Math. , vol.59 , pp. 65-79
    • Bär, C.1
  • 5
    • 0002881692 scopus 로고
    • Lower eigenvalue estimates for Dirac operators
    • C. Bär, Lower eigenvalue estimates for Dirac operators, Math. Ann. 293 (1992), 39-46
    • (1992) Math. Ann. , vol.293 , pp. 39-46
    • Bär, C.1
  • 6
    • 0002594991 scopus 로고
    • The Dirac operator on space forms of positive curvature
    • C. Bär, The Dirac operator on space forms of positive curvature, J. Math. Soc. Japan 48 (1994), 69-83
    • (1994) J. Math. Soc. Japan , vol.48 , pp. 69-83
    • Bär, C.1
  • 7
    • 17444435759 scopus 로고    scopus 로고
    • Metrics with harmonic spinors
    • C. Bär, Metrics with harmonic spinors, Geom. Funct. Anal. 6 (1996), 899-942
    • (1996) Geom. Funct. Anal. , vol.6 , pp. 899-942
    • Bär, C.1
  • 8
    • 0013298916 scopus 로고    scopus 로고
    • The Dirac operator on hyperbolic manifolds of finite volume
    • C. Bär, The Dirac operator on hyperbolic manifolds of finite volume, J. Diff. Geom. 54 (2000), 439-488
    • (2000) J. Diff. Geom. , vol.54 , pp. 439-488
    • Bär, C.1
  • 9
    • 0042941242 scopus 로고    scopus 로고
    • Extrinsic bounds for eigenvalues of the Dirac operator
    • C. Bär, Extrinsic bounds for eigenvalues of the Dirac operator, Ann. Global Anal. Geom. 16 (1998), 573-596
    • (1998) Ann. Global Anal. Geom. , vol.16 , pp. 573-596
    • Bär, C.1
  • 10
    • 0009141142 scopus 로고
    • Upper bounds of small eigenvalues of the Dirac operator and isometric immersions
    • U. Bunke, Upper bounds of small eigenvalues of the Dirac operator and isometric immersions, Ann. Glob. Anal. Geom. 9 (1991), 109-116
    • (1991) Ann. Glob. Anal. Geom. , vol.9 , pp. 109-116
    • Bunke, U.1
  • 14
    • 0030242191 scopus 로고    scopus 로고
    • On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
    • R. Camporesi and A. Higuchi, On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996), 1-18
    • (1996) J. Geom. Phys. , vol.20 , pp. 1-18
    • Camporesi, R.1    Higuchi, A.2
  • 16
    • 0013298917 scopus 로고
    • The spectrum of the Dirac operator on a simply connected compact Lie group
    • H. Fegan, The spectrum of the Dirac operator on a simply connected compact Lie group, Simon Stevin 61 (1987), 97-108
    • (1987) Simon Stevin , vol.61 , pp. 97-108
    • Fegan, H.1
  • 17
    • 0001587075 scopus 로고
    • Der erste Eigenwert des Dirac-Operators einer kompakten riemannschen mannigfaltigkeit nicht-negativer krümmung
    • T. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nicht-negativer Krümmung, Math. Nach. 97 (1980), 117-146
    • (1980) Math. Nach. , vol.97 , pp. 117-146
    • Friedrich, T.1
  • 18
    • 0002241155 scopus 로고
    • Zur abhängigkeit des Dirac-operators von der spin-struktur
    • T. Friedrich, Zur Abhängigkeit des Dirac-Operators von der Spin-Struktur, Colloq. Math. 48 (1984), 57-62
    • (1984) Colloq. Math. , vol.48 , pp. 57-62
    • Friedrich, T.1
  • 19
    • 0003315313 scopus 로고    scopus 로고
    • Dirac operators in Riemannian geometry
    • Providence, RI: American Mathematical Society
    • T. Friedrich, Dirac operators in Riemannian geometry, Graduate Studies in Mathematics. 25. Providence, RI: American Mathematical Society (2000)
    • (2000) Graduate Studies in Mathematics , vol.25
    • Friedrich, T.1
  • 20
    • 51649160427 scopus 로고
    • Groups of polynomial growth and expanding maps
    • M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53-73
    • (1981) Inst. Hautes Études Sci. Publ. Math. , vol.53 , pp. 53-73
    • Gromov, M.1
  • 22
    • 0000453368 scopus 로고
    • A conformal lower bound for the smallest eigenvalue of the Dirac operator and killing spinors
    • O. Hijazi, A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors, Comm. Math. Phys. 104 (1986), 151-162
    • (1986) Comm. Math. Phys. , vol.104 , pp. 151-162
    • Hijazi, O.1
  • 23
    • 0000814946 scopus 로고
    • Première valeur propre de l'opérateur de Dirac et hombre de Yamabe
    • Série I
    • O. Hijazi, Première valeur propre de l'opérateur de Dirac et hombre de Yamabe, C. R. Acad. Sci. Paris t. 313, Série I (1991), 865-868
    • (1991) C. R. Acad. Sci. Paris , vol.313 , pp. 865-868
    • Hijazi, O.1
  • 24
    • 33646063975 scopus 로고
    • Harmonic spinors
    • N. Hitchin, Harmonic spinors, Adv. Math. 14 (1974), 1-55
    • (1974) Adv. Math. , vol.14 , pp. 1-55
    • Hitchin, N.1
  • 25
    • 0001733303 scopus 로고
    • An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature
    • K.-D. Kirchberg, An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature, Ann. Glob. Anal. Geom. 4 (1986), 291-325
    • (1986) Ann. Glob. Anal. Geom. , vol.4 , pp. 291-325
    • Kirchberg, K.-D.1
  • 26
    • 0000986169 scopus 로고
    • Compact six-dimensional Kähler spin manifolds of positive scalar curvature with the smallest possible first eigenvalue of the Dirac operator
    • K.-D. Kirchberg, Compact six-dimensional Kähler spin manifolds of positive scalar curvature with the smallest possible first eigenvalue of the Dirac operator, Math. Ann. 282 (1988), 157-176
    • (1988) Math. Ann. , vol.282 , pp. 157-176
    • Kirchberg, K.-D.1
  • 27
    • 0039449796 scopus 로고    scopus 로고
    • The first eigenvalue of the Dirac operator on quaternionic Kähler manifolds
    • W. Kramer, U. Semmelmann, and G. Weingart, The first eigenvalue of the Dirac operator on quaternionic Kähler manifolds, Comm. Math. Phys. 199 (1998), 327-349
    • (1998) Comm. Math. Phys. , vol.199 , pp. 327-349
    • Kramer, W.1    Semmelmann, U.2    Weingart, G.3
  • 28
    • 0043211221 scopus 로고    scopus 로고
    • Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds
    • W. Kramer, U. Semmelmann, and G. Weingart, Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds, Math. Z. 230 (1999), 727-751
    • (1999) Math. Z. , vol.230 , pp. 727-751
    • Kramer, W.1    Semmelmann, U.2    Weingart, G.3
  • 31
    • 84972552860 scopus 로고
    • Eigenvalue bounds for the Dirac operator
    • J. Lott, Eigenvalue bounds for the Dirac operator, Pacific J. of Math. 125 (1986), 117-126
    • (1986) Pacific J. of Math. , vol.125 , pp. 117-126
    • Lott, J.1
  • 32
    • 0031283633 scopus 로고    scopus 로고
    • Stable norms of surfaces: Local structure of the unit ball at rational directions
    • D. Massart, Stable norms of surfaces: local structure of the unit ball at rational directions., Geom. Funct. Anal. 7 (1997), 996-1010
    • (1997) Geom. Funct. Anal. , vol.7 , pp. 996-1010
    • Massart, D.1
  • 34
    • 0013200657 scopus 로고
    • Spectre de l'opérateur de Dirac sur les espaces projectifs quaternioniens
    • J.-L. Milhorat, Spectre de l'opérateur de Dirac sur les espaces projectifs quaternioniens, C. R. Acad. Sci. Paris 1 (1992), 69-72
    • (1992) C. R. Acad. Sci. Paris , vol.1 , pp. 69-72
    • Milhorat, J.-L.1
  • 35
    • 0001010429 scopus 로고
    • Croissance des boules et des géodésiques fermées dans les nilvariétés
    • P. Pansu, Croissance des boules et des géodésiques fermées dans les nilvariétés, Ergodic Theory Dyn. Syst. 3 (1983), 415-445
    • (1983) Ergodic Theory Dyn. Syst. , vol.3 , pp. 415-445
    • Pansu, P.1
  • 36
    • 0013199736 scopus 로고    scopus 로고
    • The Dirac spectrum of Bieberbach manifolds
    • F. Pfäffle, The Dirac spectrum of Bieberbach manifolds, J. Geom. Phys. 35 (2000), 367-385
    • (2000) J. Geom. Phys. , vol.35 , pp. 367-385
    • Pfäffle, F.1
  • 37
    • 0000504799 scopus 로고
    • Regular homotopy classes of immersed surfaces
    • U. Pinkall, Regular homotopy classes of immersed surfaces, Topology 24 (1985), 421-434
    • (1985) Topology , vol.24 , pp. 421-434
    • Pinkall, U.1
  • 38
    • 0003350503 scopus 로고
    • Elliptic operators, topology and asymptotic methods
    • Longman
    • J. Roe, Elliptic operators, topology and asymptotic methods, Pitman Research Notes in Mathematics Series, no. 179, Longman, 1988
    • (1988) Pitman Research Notes in Mathematics Series , vol.179
    • Roe, J.1
  • 43
    • 0013198660 scopus 로고
    • Spektren symmetrischer räume
    • H. Strese, Spektren symmetrischer Räume, Math. Nachr. 98 (1980), 75-82
    • (1980) Math. Nachr. , vol.98 , pp. 75-82
    • Strese, H.1
  • 44
    • 0013200659 scopus 로고
    • Über den Dirac-operator auf graßmann-mannigfaltigkeiten
    • H. Strese, über den Dirac-Operator auf Graßmann-Mannigfaltigkeiten, Math. Nachr. 98 (1980), 53-59
    • (1980) Math. Nachr. , vol.98 , pp. 53-59
    • Strese, H.1
  • 47
    • 0002603037 scopus 로고
    • Spin structures on hypersurfaces and the spectrum of the Dirac operator on spheres
    • Oziewicz, Zbigniew (ed.) et al., Kluwer Academic Publishers
    • A. Trautman, Spin structures on hypersurfaces and the spectrum of the Dirac operator on spheres, In: Oziewicz, Zbigniew (ed.) et al., Spinors, Twistors, Clifford Algebras and Quantum Deformations, Kluwer Academic Publishers, 1993, 25-29
    • (1993) Spinors, Twistors, Clifford Algebras and Quantum Deformations , pp. 25-29
    • Trautman, A.1
  • 48
    • 0000268975 scopus 로고
    • The Dirac operator on hypersurfaces
    • A. Trautman, The Dirac operator on hypersurfaces, Acta Phys. Polon. B 26 (1995), 1283-1310
    • (1995) Acta Phys. Polon. B , vol.26 , pp. 1283-1310
    • Trautman, A.1


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