메뉴 건너뛰기




Volumn 54, Issue 3, 2000, Pages 439-488

The dirac operator on hyperbolic manifolds of finite volume

Author keywords

Clustering of eigenvalues; Dirac operator; Hyperbolic manifolds of finite volume; L2 spectrum; Linking numbers

Indexed keywords


EID: 0013298916     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214339790     Document Type: Article
Times cited : (56)

References (32)
  • 1
    • 0002739380 scopus 로고
    • A geometric construction of the discrete series for semisimple Lie groups
    • M. F. Atiyah & W. Schmid, A geometric construction of the discrete series for semisimple Lie groups, Invent. Math. 42 (1977) 1-62.
    • (1977) Invent. Math , vol.42 , pp. 1-62
    • Atiyah, M.F.1    Schmid, W.2
  • 2
    • 0039311578 scopus 로고
    • Erratum to the paper: A geometric construction of the discrete series forsemisimple Lie groups
    • M. F. Atiyah & W. Schmid, Erratum to the paper: A geometric construction of the discrete series for semisimple Lie groups, Invent. Math. 54 (1979) 189-192.
    • (1979) Invent. Math , vol.54 , pp. 189-192
    • Atiyah, M.F.1    Schmid, W.2
  • 4
    • 17444435759 scopus 로고    scopus 로고
    • Metrics with harmonic spinors
    • C. Bär, Metrics with harmonic spinors, Geom. Func. Anal. 6 (1996) 899-942.
    • (1996) Geom. Func. Anal , vol.6 , pp. 899-942
    • Bär, C.1
  • 6
    • 84985345727 scopus 로고
    • The spectrum of the Dirac operator on the hyperbolic space
    • U. Bunke, The spectrum of the Dirac operator on the hyperbolic space, Math. Nachr. 153 (1991) 179-190.
    • (1991) Math. Nachr , vol.153 , pp. 179-190
    • Bunke, U.1
  • 7
    • 33646022213 scopus 로고
    • The spinor heat kernel in maximally symmetric spaces
    • R. Camporesi, The spinor heat kernel in maximally symmetric spaces, Comm. Math. Phys. 148 (1992) 283-308.
    • (1992) Comm. Math. Phys , vol.148 , pp. 283-308
    • Camporesi, R.1
  • 8
    • 0030242191 scopus 로고    scopus 로고
    • On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
    • R. Camporesi & 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
  • 9
    • 84972534333 scopus 로고
    • The spectrum of degenerating hyperbolic S-manifolds
    • I. Chavel & J. Dodziuk, The spectrum of degenerating hyperbolic S-manifolds, J. Differential Geom. 39 (1994) 123-137.
    • (1994) J. Differential Geom , vol.39 , pp. 123-137
    • Chavel, I.1    Dodziuk, J.2
  • 10
    • 51249175831 scopus 로고
    • Les valeurs propres inférieures à 1/4 des surfaces de Riemann de petit rayon d’injectivité
    • B. Colbois & G. Courtois, Les valeurs propres inférieures à 1/4 des surfaces de Riemann de petit rayon d’injectivité, Comment. Math. Helv. 64 (1989) 349-362.
    • (1989) Comment. Math. Helv , vol.64 , pp. 349-362
    • Colbois, B.1    Courtois, G.2
  • 11
    • 0040847204 scopus 로고
    • Convergence de variétés et convergence du spectre du Laplacien
    • B. Colbois & G. Courtois, Convergence de variétés et convergence du spectre du Laplacien, Ann. Sci. École Norm. Sup. (4) 24 (1991) 507-518.
    • (1991) Ann.Sci. École Norm. Sup , vol.24 , Issue.4 , pp. 507-518
    • Colbois, B.1    Courtois, G.2
  • 12
    • 0010724080 scopus 로고
    • The spectrum of the Hodge Laplacian for a degenerating family of hyperbolic three manifolds
    • J. Dodziuk & J. McGowan, The spectrum of the Hodge Laplacian for a degenerating family of hyperbolic three manifolds, Trans. Amer. Math. Soc. 347 (1995) 1981-1995.
    • (1995) Trans. Amer. Math. Soc , vol.347 , pp. 1981-1995
    • Dodziuk, J.1    McGowan, J.2
  • 13
    • 34250250721 scopus 로고
    • The differential form spectrum of hyperbolic space
    • H. Donnelly, The differential form spectrum of hyperbolic space, Manuscr. Math. 33 (1980/81) 365-385.
    • (1980) Manuscr. Math , vol.33 , pp. 365-385
    • Donnelly, H.1
  • 14
    • 84972567499 scopus 로고
    • Pure point spectrum and negative curvature for noncompact manifolds
    • H. Donnelly & P. Li, Pure point spectrum and negative curvature for noncompact manifolds, Duke Math. J. 46 (1979) 497-503.
    • (1979) Duke Math. J , vol.46 , pp. 497-503
    • Donnelly, H.1    Li, P.2
  • 16
    • 0001897231 scopus 로고
    • Seminar Analysis of the Karl-Weierstraß-Institute 1986/1987 (Leipzig) (B.-W. Schulze and H. Triebei, eds.), Teubner-Verlag
    • J. Eichhorn, Elliptic differential operators on noncompact manifolds, Seminar Analysis of the Karl-Weierstraß-Institute 1986/1987 (Leipzig) (B.-W. Schulze and H. Triebei, eds.), Teubner-Verlag, 1988, 4-169.
    • (1988) Elliptic Differential Operators on Noncompact Manifolds , pp. 4-169
    • Eichhorn, J.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, Coll. Math. 48 (1984) 57-62.
    • (1984) Coll. Math , vol.48 , pp. 57-62
    • Friedrich, T.1
  • 20
    • 0039903882 scopus 로고
    • Über das absolut stetige Spektrum singulärer Differentialgleichungssysteme
    • E. Heinz, Über das absolut stetige Spektrum singulärer Differentialgleichungssysteme, Nachr. Akad. Wiss. Göttingen II 1 (1982) 1-9.
    • (1982) Nachr. Akad. Wiss. Göttingen II , vol.1 , pp. 1-9
    • Heinz, E.1
  • 21
    • 0001682039 scopus 로고
    • The remainder estimate in spectral accumulation for degenerating hyperbolic surfaces
    • L. Ji & M. Zworski, The remainder estimate in spectral accumulation for degenerating hyperbolic surfaces, J. Func. Anal. 114 (1993) 412-420.
    • (1993) J. Func. Anal , vol.114 , pp. 412-420
    • Ji, L.1    Zworski, M.2
  • 24
    • 84974002892 scopus 로고
    • Hodge theory on hyperbolic manifolds
    • R. Mazzeo & R. S. Phillips, Hodge theory on hyperbolic manifolds, Duke Math. J. 60 (1990) 509-559.
    • (1990) Duke Math. J , vol.60 , pp. 509-559
    • Mazzeo, R.1    Phillips, R.S.2
  • 25
    • 0007188175 scopus 로고
    • Manifolds with cusps of rank one, Springer
    • Berlin
    • W. Müller, Manifolds with cusps of rank one, Springer, Lecture Notes in Math. 1244, Berlin, 1987.
    • (1987) Lecture Notes in Math , vol.1244
    • Müller, W.1
  • 29
    • 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
  • 30
    • 0000287293 scopus 로고
    • Oszillationsmethoden für Systeme gewöhnlicher Differentialgleichungen
    • J. Weidmann, Oszillationsmethoden für Systeme gewöhnlicher Differentialgleichungen, Math. Z. 119 (1971) 349-373.
    • (1971) Math. Z , vol.119 , pp. 349-373
    • Weidmann, J.1
  • 32
    • 0012843117 scopus 로고
    • Absolut stetiges Spektrum bei Sturm-Liouville-Operatoren und Dirac-Systemen
    • J. Weidmann, Absolut stetiges Spektrum bei Sturm-Liouville-Operatoren und Dirac-Systemen, Math. Z. 180 (1982) 423-427.
    • (1982) Math. Z , vol.180 , pp. 423-427
    • Weidmann, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.