|
On the convergence in capacity on compact Kahler manifolds and its applications
Author(s):
Pham
Hoang
Hiep
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2007-2018.
MSC (2000):
Primary 32W20;
Secondary 32Q15
Posted:
February 12, 2008
MathSciNet review:
2383507
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
The main aim of the present note is to study the convergence in  on a compact Kahler mainfold  . The obtained results are used to study global extremal functions and describe the  -pluripolar hull of an  -pluripolar subset in  .
References:
-
- [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
 , 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:
10.1090/S0002-9939-08-09043-6
PII:
S 0002-9939(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
Posted:
February 12, 2008
Additional Notes:
This work is supported by the National Research Program for Natural Sciences, Vietnam.
Communicated by:
Mei-Chi Shaw
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
