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$ \overline\partial$-equation on a lunar domain with mixed boundary conditions


Authors: Xiaojun Huang and Xiaoshan Li
Journal: Trans. Amer. Math. Soc. 368 (2016), 6915-6937
MSC (2010): Primary 32W05; Secondary 32V15
DOI: https://doi.org/10.1090/tran/6547
Published electronically: February 10, 2016
MathSciNet review: 3471081
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, making use of the method developed by Catlin, we study the $ L^2$-estimate for the $ \bar \partial $-equation on a lunar manifold with mixed boundary conditions.


References [Enhancements On Off] (What's this?)

  • [Cat] David Catlin, Sufficient conditions for the extension of CR structures, J. Geom. Anal. 4 (1994), no. 4, 467-538. MR 1305993 (95j:32028), https://doi.org/10.1007/BF02922141
  • [Cho] Sanghyun Cho, Extension of CR structures on pseudoconvex CR manifolds with one degenerate eigenvalue, Tohoku Math. J. (2) 55 (2003), no. 3, 321-360. MR 1993860 (2004f:32048)
  • [CC] David W. Catlin and Sanghyun Cho, Extension of CR structures on three dimensional compact pseudoconvex CR manifolds, Math. Ann. 334 (2006), no. 2, 253-280. MR 2207699 (2007a:32037), https://doi.org/10.1007/s00208-005-0716-5
  • [CS] So-Chin Chen and Mei-Chi Shaw, Partial differential equations in several complex variables, AMS/IP Studies in Advanced Mathematics, vol. 19, American Mathematical Society, Providence, RI; International Press, Boston, MA, 2001. MR 1800297 (2001m:32071)
  • [CSh] Debraj Chakrabarti and Mei-Chi Shaw, $ L^2$ Serre duality on domains in complex manifolds and applications, Trans. Amer. Math. Soc. 364 (2012), no. 7, 3529-3554. MR 2901223, https://doi.org/10.1090/S0002-9947-2012-05511-5
  • [DE] J. P. Demailly, Complex Analytic and Differential Geometry, Monograph Grenoble, 1997.
  • [FK] G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Annals of Mathematics Studies, No. 75. MR 0461588 (57 #1573)
  • [HLY] Xiaojun Huang, Hing-Sun Luk, and Stephen S. T. Yau, On a CR family of compact strongly pseudoconvex CR manifolds, J. Differential Geom. 72 (2006), no. 3, 353-379. MR 2219938 (2007g:32025)
  • [Ho1] Lars Hörmander, $ L^{2}$ estimates and existence theorems for the $ \bar \partial $ operator, Acta Math. 113 (1965), 89-152. MR 0179443 (31 #3691)
  • [Ho2] Lars Hörmander, An introduction to complex analysis in several variables, 3rd ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR 1045639 (91a:32001)
  • [Li] X. Li, Ph.D. Thesis, Wuhan University, 2014. (to appear)

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Additional Information

Xiaojun Huang
Affiliation: School of Mathematics and Statistics, Wuhan University, Hubei 430072, People’s Republic of China – and – Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: huangx@math.rutgers.edu

Xiaoshan Li
Affiliation: School of Mathematics and Statistics, Wuhan University, Hubei 430072, People’s Republic of China
Email: xiaoshanli@whu.edu.cn

DOI: https://doi.org/10.1090/tran/6547
Keywords: $\overline\partial$-operator, $L^2$-estimate, $\overline\partial$-Dirichlet boundary condition, $\overline\partial$-Neumann boundary condition
Received by editor(s): March 4, 2014
Received by editor(s) in revised form: August 20, 2014
Published electronically: February 10, 2016
Additional Notes: The first author was supported in part by NSF-1363418
The second author was supported by the China Scholarship Council and the Fundamental Research Fund for the Central Universities
Article copyright: © Copyright 2016 American Mathematical Society

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