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ISSN 1088-9485(e) ISSN 0273-0979(p)

Book Review

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Book Information

Author(s): Sorin Dragomir and Giuseppe Tomassini
Title: Differential geometry and analysis on CR manifolds
Additional book information: Progress in Mathematics, vol. 246, Birkhäuser, Basel, 2006, xiv+487 pp., US$109.00, ISBN 978-0-8176-4388-1

References:

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2.: A. Andreotti and C. D. Hill, Complex characteristic coordinates and the tangential Cauchy-Riemann equations, Ann. Scuola Norm. Pisa 26(1972), 299-324. MR 0460724 (57:717)
3.: M. S. Baouendi, P. F. Ebenfelt, and L. P. Rothschild, Real submanifolds in complex space and their mappings, Princeton Mathematical Series, vol. 47, Princeton Univ. Press, Princeton, NJ, 1999. MR 1668103 (2000b:32066)
4.: A. Boggess, CR manifolds and the tangential Cauchy-Riemann complex, Studies in Advanced Math., CRC Press, Boca Raton, Fla., 1991. MR 1211412 (94e:32035)
5.: D. Catlin, Sufficient conditions for the extension of CR structures, J. Geom. Anal. 4 (1994), 467-538. MR 1305993 (95j:32028)
6.: S. S. Chern and J. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133(1974), 219-271. MR 0425155 (54:13112)
7.: J. P. D'Angelo, Several complex variables and the geometry of real hypersurfaces, Studies in Advanced Math., CRC Press, Boca Raton, Fla., 1993. MR 1224231 (94i:32022)
8.: C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26(1974), 1-65. MR 0350069 (50:2562)
9.: C. Fefferman, Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains, Annals of Math. (2) 103(1976), 395-416; 104(1976), 393-394. MR 0407321 (53:11097b)
10.: G. B. Folland and E. M. Stein, Estimates for the ${\partial}_b$ -complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27(1974), 429-522. MR 0367477 (51:3719)
11.: H. Jacobowitz, An introduction to CR structures, Mathematical Surveys and Monographs, No. 32, Amer. Math. Soc., Providence, RI, 1990. MR 1067341 (93h:32023)
12.: D. Jerison and J. M. Lee, The Yamabe problem on CR manifolds, J. Diff. Geom. 25(1987), 167-197. MR 880182 (88i:58162)
13.: J. M. Lee, The Fefferman metric and pseudo-Hermitian invariants, Trans. Amer. Math. Soc. 296(1986), 411-429. MR 837820 (87j:32063)
14.: J. M. Lee and T. Parker, The Yamabe problem, Bull. Amer. Soc. 17(1987), 37-91. MR 888880 (88f:53001)
15.: H. Lewy, On the local character of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Annals of Math. 64(1956), 514-522. MR 0081952 (18:473b)
16.: H. Lewy, An example of a smooth linear partial differential equation without solution, Annals of Math. 66(1957), 155-158. MR 0088629 (19:551d)
17.: A. Newlander and L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Annals of Math. (2) 65(1957), 391-404. MR 0088770 (19:577a)
18.: N. Tanaka, A differential geometric study on strongly pseudo-convex manifolds, Kinokuniya Book Store Co., Ltd., Kyoto, 1975. MR 0399517 (53:3361)
19.: S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Diff. Geom. 13(1978), 25-41. MR 520599 (80e:32015)
20.: S. M. Webster, On the proof of Kuranishi's embedding theorem, Ann. Inst. Henri Poincaré 6(1989), no. 3, 183-207 (French summary). MR 0995504 (90h:32042b)

Additional Information:

Reviewer(s):
John P. D'Angelo
Affiliation: University of Illinois, Urbana
Email: jpda@math.uiuc.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 45 (2008), 177-183.

MSC (2000): Primary 32T15, 32V05, 32V15, 32V20, 35B65, 35D05, 35D10, 53C07, 53C10, 53C12, 53C17, 53C21, 53C25, 53C26, 53C40, 53C43, 53C50, 53D10
PII: S 0273-0979(07)01160-3
Posted: May 1, 2007
Additional notes: The reviewer was partially supported by NSF Grant DMS 05-00765.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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