Hodge theory on hyperbolic manifolds
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Duke Mathematical Journal

Hodge theory on hyperbolic manifolds

Rafe Mazzeo and Ralph S. Phillips

Source: Duke Math. J. Volume 60, Number 2 (1990), 509-559.

First Page PDF: View first page of article (PDF, 79 KB)

Primary Subjects: 58A14
Secondary Subjects: 58G25

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077297303
Mathematical Reviews number (MathSciNet): MR1047764
Zentralblatt MATH identifier: 0712.58006
Digital Object Identifier: doi:10.1215/S0012-7094-90-06021-1

References

[A1] M. T. Anderson, $L^{2}$ Harmonic Forms on Complete Riemannian Manifolds, Geometry and Analysis on Manifolds (Katata/Kyoto, 1987) ed. T. Sunada, Lecture Notes in Math., vol. 1339, Springer-Verlag, Berlin, 1988, pp. 1–19.
Mathematical Reviews (MathSciNet): MR89j:58004
Zentralblatt MATH: 0652.53030
Digital Object Identifier: doi:10.1007/BFb0083043
[A2] Michael T. Anderson, $L\sp 2$ harmonic forms and a conjecture of Dodziuk-Singer, Bull. Amer. Math. Soc. (N.S.) 13 (1985), no. 2, 163–165.
Mathematical Reviews (MathSciNet): MR87a:58153
Zentralblatt MATH: 0573.53025
Digital Object Identifier: doi:10.1090/S0273-0979-1985-15405-9
Project Euclid: euclid.bams/1183552701
[B-S] A. Borel and J. P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436–491.
Mathematical Reviews (MathSciNet): MR52:8337
Zentralblatt MATH: 0274.22011
Digital Object Identifier: doi:10.1007/BF02566134
[B-T] R. Bott and L. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York, 1982.
Mathematical Reviews (MathSciNet): MR83i:57016
Zentralblatt MATH: 0496.55001
[dR] G. de Rham, Differentiable Manifolds, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 266, Springer-Verlag, Berlin, 1984.
Mathematical Reviews (MathSciNet): MR85m:58005
Zentralblatt MATH: 0534.58003
[Do1] J. Dodziuk, $L^{2}$ Harmonic forms on complete manifolds, Ann. of Math. Studies 102 (1982), 292–302.
Zentralblatt MATH: 0484.53033
[Do2] J. Dodziuk, $L^{2}$ harmonic forms on rotationally symmetric Riemannian manifolds, Proc. Amer. Math. Soc. 77 (1979), no. 3, 395–400.
Mathematical Reviews (MathSciNet): MR81e:58004
Zentralblatt MATH: 0423.58002
Digital Object Identifier: doi:10.2307/2042193
JSTOR: links.jstor.org
[D1] H. Donnelly, The differential form spectrum of hyperbolic space, Manuscripta Math. 33 (1981), no. 3-4, 365–385.
Mathematical Reviews (MathSciNet): MR82f:58085
Zentralblatt MATH: 0464.58020
Digital Object Identifier: doi:10.1007/BF01798234
[D2] H. Donnelly, On the essential spectrum of a complete Riemannian manifold, Topology 20 (1981), no. 1, 1–14.
Mathematical Reviews (MathSciNet): MR81j:58081
Zentralblatt MATH: 0463.53027
Digital Object Identifier: doi:10.1016/0040-9383(81)90012-4
[D-X] H. Donnelly and F. Xavier, On the differential form spectrum of negatively curved Riemannian manifolds, Amer. J. Math. 106 (1984), no. 1, 169–185.
Mathematical Reviews (MathSciNet): MR85i:58115
Zentralblatt MATH: 0547.58034
Digital Object Identifier: doi:10.2307/2374434
JSTOR: links.jstor.org
[E] C. Epstein, The spectral theory of geometrically periodic hyperbolic $3$-manifolds, Mem. Amer. Math. Soc. 58 (1985), no. 335, ix+161.
Mathematical Reviews (MathSciNet): MR87b:58088
Zentralblatt MATH: 0584.58047
[G1] M. Gaffney, A special Stokes's Theorem for complete Riemannian manifolds, Ann. of Math. (2) 60 (1954), 140–145.
Mathematical Reviews (MathSciNet): MR15,986d
Zentralblatt MATH: 0055.40301
Digital Object Identifier: doi:10.2307/1969703
JSTOR: links.jstor.org
[G2] M. Gaffney, The harmonic operator for exterior differential forms, Proc. Nat. Acad. Sci. U. S. A. 37 (1951), 48–50.
Mathematical Reviews (MathSciNet): MR13,987b
Zentralblatt MATH: 0042.10205
Digital Object Identifier: doi:10.1073/pnas.37.1.48
[Mas] B. Maskit, On Poincaré's theorem for fundamental polygons, Advances in Math. 7 (1971), 219–230.
Mathematical Reviews (MathSciNet): MR45:7049
Zentralblatt MATH: 0223.30008
Digital Object Identifier: doi:10.1016/S0001-8708(71)80003-8
[M1] R. Mazzeo, Hodge cohomology of negatively curved manifolds, Ph.D. thesis, MIT, 1986.
[M2] R. Mazzeo, The Hodge cohomology of a conformally compact metric, J. Differential Geom. 28 (1988), no. 2, 309–339.
Mathematical Reviews (MathSciNet): MR89i:58005
Zentralblatt MATH: 0656.53042
Project Euclid: euclid.jdg/1214442281
[M3] R. Mazzeo, Unique Continuation of Infinity and Embedded Eigenvalues for Asymptotically Hyperbolic Manifolds, Preprint.
[Me] R. Melrose, Analysis on Manifolds with Corners, Lecture Notes, MIT, 1988.
[Th] W. Thurston, The Geometry and Topology of $3$-Manifolds, Princeton University.
[Z] S. Zucker, $L\sb{2}$ cohomology of warped products and arithmetic groups, Invent. Math. 70 (1982/83), no. 2, 169–218.
Mathematical Reviews (MathSciNet): MR86j:32063
Zentralblatt MATH: 0508.20020
Digital Object Identifier: doi:10.1007/BF01390727

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