Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the convergence in capacity on compact Kahler manifolds and its applications


Author: Pham Hoang Hiep
Journal: Proc. Amer. Math. Soc. 136 (2008), 2007-2018
MSC (2000): Primary 32W20; Secondary 32Q15
DOI: https://doi.org/10.1090/S0002-9939-08-09043-6
Published electronically: February 12, 2008
MathSciNet review: 2383507
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main aim of the present note is to study the convergence in $ C_{X,\omega }$ on a compact Kahler mainfold $ X$. The obtained results are used to study global extremal functions and describe the $ \omega $-pluripolar hull of an $ \omega $-pluripolar subset in $ X$.


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

  • [Bl] Z. Blocki, Uniqueness and stability for the complex Monge-Ampère equation on compact Kahler manifolds, Indiana Univ. Math. J. 52 (2003), no. 6, 1697-1701. MR 2021054 (2004m:32073)
  • [BT1] E. Bedford and B. A. Taylor, The Dirichlet problem for the complex Monge-Ampère operator, Invent. Math. 37 (1976), 1-44. MR 0445006 (56:3351)
  • [BT2] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. MR 674165 (84d:32024)
  • [BT3] E. Bedford and B. A. Taylor, Plurisubhurmonic functions with logarithmic singularities, Ann. Inst. Fourier 38 (1988), 133-171. MR 978244 (90f:32016)
  • [BT4] E. Bedford and B. A. Taylor, Uniqueness for the complex Monge-Ampère equation for functions of logarithmic growth, Indiana Univ. Math. J. 38 (1989), 455-469. MR 997391 (90i:32025)
  • [Ce1] U. Cegrell, Pluricomplex energy, Acta Mathematica 180 (1998), 187-217. MR 1638768 (99h:32016)
  • [Ce2] U. Cegrell, The general definition of the complex Monge-Ampère operator, Ann. Inst. Fourier (Grenoble) 54 (2004), 159-179. MR 2069125 (2005d:32062)
  • [Ce3] U. Cegrell, Convergence in capacity, Technical report, Issac Newton Institute for Mathematical Sciences, 2001.
  • [GZ] V. Guedj and A. Zeriahi, Intrinsic capacities on compact Kahler manifolds, J. Geom. Anal. 15 (2005), no. 4, 607-639. MR 2203165 (2006j:32041)
  • [Ho] L. Hörmander, Notions of Convexity, Progress in Mathematics 127, Birkhäuser, Boston, 1994. MR 1301332 (95k:00002)
  • [Ko1] S. Kołodziej, Capacities associated to the Siciak extremal function, Ann. Polon. Math. XLIX (1989), 279-290. MR 997520 (90h:32039)
  • [Ko2] S. Kołodziej, The Monge-Ampère equation on compact Kahler manifolds, Indiana Univ. Math. J. 52 (2003), 667-686. MR 1986892 (2004i:32062)
  • [Si] J. Siciak, Extremal plurisubharmonic functions in $ \mathbf{C}^{n}$, Ann. Polon. Math. XXXIX (1981), 175-210. MR 617459 (83e:32018)
  • [Xi1] Y. Xing, Continuity of the complex Monge-Ampère operator, Proc. Amer. Math. Soc. 124 (1996), 457-467. MR 1322940 (96d:32015)
  • [Xi2] Y. Xing, Complex Monge-Ampère measures of pluriharmonic functions with bounded values near the boundary, Canad. J. Math. 52 (2000), 1085-1100. MR 1782339 (2001h:32070)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32W20, 32Q15

Retrieve articles in all journals with MSC (2000): 32W20, 32Q15


Additional Information

Pham Hoang Hiep
Affiliation: Department of Mathematics, University of Education (Dai hoc Su Pham Ha Noi), CauGiay, Hanoi, Vietnam
Email: phhiep_vn@yahoo.com

DOI: https://doi.org/10.1090/S0002-9939-08-09043-6
Keywords: Complex Monge-Amp\`{e}re operator, $\omega$-plurisubharmonic functions, compact Kahler manifold
Received by editor(s): September 30, 2006
Received by editor(s) in revised form: December 11, 2006
Published electronically: February 12, 2008
Additional Notes: This work is supported by the National Research Program for Natural Sciences, Vietnam.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society