On the convergence in capacity on compact Kahler manifolds and its applications
HTML articles powered by AMS MathViewer
- by Pham Hoang Hiep
- Proc. Amer. Math. Soc. 136 (2008), 2007-2018
- DOI: https://doi.org/10.1090/S0002-9939-08-09043-6
- Published electronically: February 12, 2008
- PDF | Request permission
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
- Zbigniew Błocki, Uniqueness and stability for the complex Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J. 52 (2003), no. 6, 1697–1701. MR 2021054, DOI 10.1512/iumj.2003.52.2346
- Eric Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), no. 1, 1–44. MR 445006, DOI 10.1007/BF01418826
- Eric Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), no. 1-2, 1–40. MR 674165, DOI 10.1007/BF02392348
- E. Bedford and B. A. Taylor, Plurisubharmonic functions with logarithmic singularities, Ann. Inst. Fourier (Grenoble) 38 (1988), no. 4, 133–171 (English, with French summary). MR 978244, DOI 10.5802/aif.1152
- Eric Bedford and B. A. Taylor, Uniqueness for the complex Monge-Ampère equation for functions of logarithmic growth, Indiana Univ. Math. J. 38 (1989), no. 2, 455–469. MR 997391, DOI 10.1512/iumj.1989.38.38021
- Urban Cegrell, Pluricomplex energy, Acta Math. 180 (1998), no. 2, 187–217. MR 1638768, DOI 10.1007/BF02392899
- Urban Cegrell, The general definition of the complex Monge-Ampère operator, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 1, 159–179 (English, with English and French summaries). MR 2069125, DOI 10.5802/aif.2014
- U. Cegrell, Convergence in capacity, Technical report, Issac Newton Institute for Mathematical Sciences, 2001.
- Vincent Guedj and Ahmed Zeriahi, Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal. 15 (2005), no. 4, 607–639. MR 2203165, DOI 10.1007/BF02922247
- Lars Hörmander, Notions of convexity, Progress in Mathematics, vol. 127, Birkhäuser Boston, Inc., Boston, MA, 1994. MR 1301332
- S. Kołodziej, Capacities associated to the Siciak extremal function, Ann. Polon. Math. 49 (1989), no. 3, 279–290. MR 997520, DOI 10.4064/ap-49-3-279-290
- Sławomir Kołodziej, The Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J. 52 (2003), no. 3, 667–686. MR 1986892, DOI 10.1512/iumj.2003.52.2220
- Józef Siciak, Extremal plurisubharmonic functions in $\textbf {C}^{n}$, Ann. Polon. Math. 39 (1981), 175–211. MR 617459, DOI 10.4064/ap-39-1-175-211
- Yang Xing, Continuity of the complex Monge-Ampère operator, Proc. Amer. Math. Soc. 124 (1996), no. 2, 457–467. MR 1322940, DOI 10.1090/S0002-9939-96-03316-3
- Yang Xing, Complex Monge-Ampère measures of plurisubharmonic functions with bounded values near the boundary, Canad. J. Math. 52 (2000), no. 5, 1085–1100. MR 1782339, DOI 10.4153/CJM-2000-045-x
Bibliographic 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
- 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
- © 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), 2007-2018
- MSC (2000): Primary 32W20; Secondary 32Q15
- DOI: https://doi.org/10.1090/S0002-9939-08-09043-6
- MathSciNet review: 2383507