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The Serre duality theorem for a non-compact weighted CR manifold
Author(s):
Mitsuhiro
Itoh;
Jun
Masamune;
Takanari
Saotome
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3539-3548.
MSC (2000):
Primary 32V20, 53C17;
Secondary 58A14, 14F15
Posted:
June 11, 2008
MathSciNet review:
2415038
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Additional information
Abstract:
It is proved that the Hodge decomposition and Serre duality hold on a non-compact weighted CR manifold with negligible boundary. A complete CR manifold has negligible boundary. Some examples of complete CR manifolds are presented.
References:
-
- 1.
- M. Biroli and U. Mosco, A Saint-Venant type principle for Dirichlet forms on discontinuous media, Annali di Matematica pura ed applicatata (1995), IV, 125-181. MR 1378473 (97b:35082)
- 2.
- A. Boggess, CR manifolds and the tangential Cauchy-Riemann complex. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1991. MR 1211412 (94e:32035)
- 3.
- D.E. Blair, Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, Berlin-New York, 1976. MR 0467588 (57:7444)
- 4.
- W. Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math. Ann. 117, (1939). 98-105. MR 0001880 (1:313d)
- 5.
- G.B. Folland and J.J. Kohn, The Neumann problem for the Cauchy-Riemann complex. Annals of Mathematics Studies, No. 75. Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1972. MR 0461588 (57:1573)
- 6.
- C.D. Hill and M. Nacinovich, Duality and distribution cohomology for
 manifolds, Ann. Scuola Norm. Sup. Pisa XXII (1995), 315-339. MR 1354910 (97g:32007) - 7.
- L. Hörmander, Hypoelliptic second order differential equations. Acta Math. 119 (1967), 147-171. MR 0222474 (36:5526)
- 8.
- M. Itoh and T. Saotome, The Serre duality for holomorphic vector bundles over a strongly pseudo-convex manifold, Tsukuba J. Math. 31 (2007), no. 1. 197-204. MR 2337126
- 9.
- A. Isaev, Lectures on the automorphism groups of Kobayashi-Hyperbolic manifolds, Lecture Notes in Mathematics, Vol. 1902 (2007), VIII. MR 2352328
- 10.
- J.J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds, I, Ann. Math. 78 (1963), 112-148; II, ibid, 79 (1964), 450-472. MR 0153030 (27:2999), MR 0208200 (34:8010)
- 11.
- J.J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. MR 0181815 (31:6041)
- 12.
- J. Masamune, Essential self-adjointness of a sublaplacian via heat equation, Comm. Partial Differential Equations 30 (2005), no. 11, 1595-1609. MR 2182306 (2006h:35035)
- 13.
- J. Masamune, Vanishing and conservativeness of harmonic forms of a non-compact CR manifold, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008), no. 2, 79-102.
- 14.
- M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness. Academic Press, New York-London, 1975. MR 0493420 (58:12429b)
- 15.
- N. Tanaka, A differential geometric study on strongly pseudoconvex CR manifolds, Kinokuniya Book Store Co., Ltd., Kyoto, 1975. MR 0399517 (53:3361)
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Additional Information:
Mitsuhiro
Itoh
Affiliation:
Institute of Mathematics, University of Tsukuba, 305-8751, Tsukuba, Japan
Email:
itohm@sakura.cc.tsukuba.ac.jp
Jun
Masamune
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280
Email:
masamune@wpi.edu
Takanari
Saotome
Affiliation:
Graduate School of Pure and Applied Sciences, University of Tsukuba, 305-8571, Tsukuba, Japan
Email:
tsaotome@math.tsukuba.ac.jp
DOI:
10.1090/S0002-9939-08-09498-7
PII:
S 0002-9939(08)09498-7
Keywords:
Strongly pseudo-convex manifold,
CR manifold,
Serre duality,
Hodge decomposition,
Witten-Kohn Laplacian,
weighted Laplacian
Received by editor(s):
July 17, 2007
Posted:
June 11, 2008
Communicated by:
Mikhail Shubin
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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