The Serre duality theorem for a non-compact weighted CR manifold
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- by Mitsuhiro Itoh, Jun Masamune and Takanari Saotome PDF
- Proc. Amer. Math. Soc. 136 (2008), 3539-3548 Request permission
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
- M. Biroli and U. Mosco, A Saint-Venant type principle for Dirichlet forms on discontinuous media, Ann. Mat. Pura Appl. (4) 169 (1995), 125–181 (English, with English and Italian summaries). MR 1378473, DOI 10.1007/BF01759352
- Albert Boggess, CR manifolds and the tangential Cauchy-Riemann complex, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1991. MR 1211412
- David E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin-New York, 1976. MR 0467588
- Wei-Liang Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann. 117 (1939), 98–105 (German). MR 1880, DOI 10.1007/BF01450011
- 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, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588
- C. Denson Hill and M. Nacinovich, Duality and distribution cohomology of CR manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 (1995), no. 2, 315–339. MR 1354910
- Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
- Mitsuhiro Itoh and Takanari Saotome, The Serre duality theorem for holomorphic vector bundles over a strongly pseudo-convex manifold, Tsukuba J. Math. 31 (2007), no. 1, 197–204. MR 2337126, DOI 10.21099/tkbjm/1496165121
- Alexander Isaev, Lectures on the automorphism groups of Kobayashi-hyperbolic manifolds, Lecture Notes in Mathematics, vol. 1902, Springer, Berlin, 2007. MR 2352328
- J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds. I, Ann. of Math. (2) 78 (1963), 112–148. MR 153030, DOI 10.2307/1970506
- J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443–492. MR 181815, DOI 10.1002/cpa.3160180305
- Jun Masamune, Essential self-adjointness of a sublaplacian via heat equation, Comm. Partial Differential Equations 30 (2005), no. 10-12, 1595–1609. MR 2182306, DOI 10.1080/03605300500299935
- 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.
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
- Noboru Tanaka, A differential geometric study on strongly pseudo-convex manifolds, Lectures in Mathematics, Department of Mathematics, Kyoto University, No. 9, Kinokuniya Book Store Co., Ltd., Tokyo, 1975. MR 0399517
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
- Received by editor(s): July 17, 2007
- Published electronically: June 11, 2008
- Communicated by: Mikhail Shubin
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3539-3548
- MSC (2000): Primary 32V20, 53C17; Secondary 58A14, 14F15
- DOI: https://doi.org/10.1090/S0002-9939-08-09498-7
- MathSciNet review: 2415038