Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

A note on the geometry of pseudoconvex domains of finite type in almost complex manifolds

Author: Florian Bertrand
Journal: Proc. Amer. Math. Soc. 140 (2012), 1633-1641
MSC (2000): Primary 32Q60, 32T25, 32T40, 32Q45, 32Q65
Posted: August 19, 2011
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $D=\{\rho<0\}$ be a smooth domain of finite type in an almost complex manifold of real dimension four. We assume that the defining function $\rho$ is -plurisubharmonic on a neighborhood of $\overline{D}$ . We study the asymptotic behavior of pseudoholomorphic discs contained in the domain .

References

Bibliography

1. F. Berteloot, Principe de Bloch et estimations de la métrique de Kobayashi des domaines de 𝐂², J. Geom. Anal. 13 (2003), no. 1, 29–37 (French, with French summary). MR 1967034 (2004a:32018), http://dx.doi.org/10.1007/BF02930994
2. Florian Bertrand, Pseudoconvex regions of finite D’Angelo type in four dimensional almost complex manifolds, Math. Z. 264 (2010), no. 2, 423–457. MR 2574983 (2011a:32042), http://dx.doi.org/10.1007/s00209-008-0471-x
3. David W. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z. 200 (1989), no. 3, 429–466. MR 978601 (90e:32029), http://dx.doi.org/10.1007/BF01215657
4. John P. D’Angelo, Finite type conditions for real hypersurfaces, J. Differential Geom. 14 (1979), no. 1, 59–66 (1980). MR 577878 (82a:32022)
5. Hervé Gaussier and Alexandre Sukhov, Estimates of the Kobayashi-Royden metric in almost complex manifolds, Bull. Soc. Math. France 133 (2005), no. 2, 259–273 (English, with English and French summaries). MR 2172267 (2006f:32036)
6. Ian Graham, Boundary behavior of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains in 𝐶ⁿ with smooth boundary, Trans. Amer. Math. Soc. 207 (1975), 219–240. MR 0372252 (51 #8468)
7. Sergey Ivashkovich and Jean-Pierre Rosay, Schwarz-type lemmas for solutions of \𝑜𝑣𝑒𝑟𝑙𝑖𝑛𝑒∂-inequalities and complete hyperbolicity of almost complex manifolds, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 7, 2387–2435 (2005) (English, with English and French summaries). MR 2139698 (2006a:32032)
8. Albert Nijenhuis and William B. Woolf, Some integration problems in almost-complex and complex manifolds., Ann. of Math. (2) 77 (1963), 424–489. MR 0149505 (26 #6992)
9. Jean-Claude Sikorav, Some properties of holomorphic curves in almost complex manifolds, Holomorphic curves in symplectic geometry, Progr. Math., vol. 117, Birkhäuser, Basel, 1994, pp. 165–189. MR 1274929

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32Q60, 32T25, 32T40, 32Q45, 32Q65

Retrieve articles in all journals with MSC (2000): 32Q60, 32T25, 32T40, 32Q45, 32Q65

Additional Information

Florian Bertrand
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: bertrand@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11016-5
PII: S 0002-9939(2011)11016-5
Keywords: Almost complex structure, Kobayashi pseudometric, D’Angelo type
Received by editor(s): August 17, 2010
Received by editor(s) in revised form: January 11, 2011
Posted: August 19, 2011
Communicated by: Franc Forsternic
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|