- 1、本文档共16页,可阅读全部内容。
- 2、有哪些信誉好的足球投注网站(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
- 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
Continuity of the Complex Monge-Ampere Operator on Compact Kahler Manifolds
a
r
X
i
v
:
m
a
t
h
/
0
7
0
3
7
5
5
v
3
[
m
a
t
h
.C
V
]
9
A
p
r
2
0
0
7
Continuity of the Complex Monge-Ampe?re
Operator on Compact Ka?hler Manifolds
Yang Xing
Abstract. We prove several approximation theorems of the complex Monge-Ampe?re
operator on a compact Ka?hler manifold. As an application we give a new proof of
a recent result of Guedj and Zeriahi on a complete description of the range of the
complex Monge-Ampe?re operator in the class of ω-plurisubharmonic functions with
vanishing complex Monge-Ampe?re mass on all pluripolar sets. As a by-product we
obtain a stability theorem of solutions of complex Monge-Ampe?re equations in some
subclass.
1. Introduction
Let X be a compact connected Ka?hler manifold of complex dimension n, equipped
with the fundamental form ω given in local coordinates by
ω =
i
2
∑
α,β
gαβ?dz
α ∧ dz?β ,
where (gαβ?) is a positive definite Hermitian matrix and dω = 0. The smooth volume
form associated to this Ka?hler metric is given by the nth wedge product ωn. Denote by
PSH(X,ω) the set of upper semi-continuous functions u : X → R ∩ {?∞} such that u is
integrable in X with respect to the volume form ωn and ω + ddcu ≥ 0 on X . Functions
in PSH(X,ω) are called ω-plurisubharmonic functions, which are defined on the whole X
and locally given by the sum of a true plurisubharmonic function and a smooth function.
Following the fundamental work of Bedford and Taylor [BT1], we know that the complex
Monge-Ampe?re operator (ω + ddc)n is well-defined for all bounded ω-plurisubharmonic
functions in X . By the Stokes theorem we always have
∫
X
(ω + ddcu)n =
∫
X
ωn. It
Yang Xing
Department of Mathematics, University of Ume?a, S-901 87 Ume?a, Sweden
E-mail address: Yang.Xing@mathdept.umu.se
2000 Mathematics Subject Classification. Primary 32W20, 32Q15
Key words. complex Monge-Ampe?re operator, compact Ka?hler manifold
1
is also known that the complex Monge-Ampe?re operator (ω + ddc)n does not make sense
without any problem for all functions in PS
您可能关注的文档
- Characterizing packet audio streams from internet multimedia applications.pdf
- Charge amplification concepts for direction-sensitive dark matter detectors.pdf
- Charge carriers of different origin in cuprates as revealed by experiment.pdf
- Charge collective modes in an incommensurately modulated cuprate.pdf
- Charge exchange for medium energy He and Ne ions in a large-angle collision at solid surfaces.pdf
- Charge transport along the c-axis in high-T_c cuprates.pdf
- Charge-sensitive TCP and rate control in the internet.pdf
- Charmless 2- and 3-body B decays and the angle alpha (phi2).pdf
- Checking Secure Interactions of Smart Card.pdf
- Chemical composition of Galactic OB stars II. The fast rotator Z Oph.pdf
文档评论(0)