Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function
(1999) In Annales Polonici Mathematici 71(1). p.87-103- Abstract
- Let
be a bounded domain in CN. Let z be a point in
and let Jz be the set of all Jensen
measures on
with barycenter at z with respect to the space of functions continuous on
and
plurisubharmonic in
. The authors prove that
is hyperconvex if and only if, for every z 2 @
,
measures in Jz are supported by @
. From this they deduce that a pluricomplex Green function
g(z,w) with its pole at w continuously extends to @
with zero boundary values if and only if
is hyperconvex.
Then the authors give a criterion for Reinhardt domains to be hyperconvex and explicitly compute
the... (More) - Let
be a bounded domain in CN. Let z be a point in
and let Jz be the set of all Jensen
measures on
with barycenter at z with respect to the space of functions continuous on
and
plurisubharmonic in
. The authors prove that
is hyperconvex if and only if, for every z 2 @
,
measures in Jz are supported by @
. From this they deduce that a pluricomplex Green function
g(z,w) with its pole at w continuously extends to @
with zero boundary values if and only if
is hyperconvex.
Then the authors give a criterion for Reinhardt domains to be hyperconvex and explicitly compute
the pluricomplex Green function on the Hartogs triangle.
The last sections are devoted to the boundary behaviour of pluricomplex Green functions. Such
a function has Property (P0) at a point w0 2 @
if limw!w0 g(z,w) = 0 for every z 2
. If the
convergence is uniform in z on compact subsets of
r{w0}, then w0 has Property (P0). Several
sufficient conditions for points on the boundary with these properties are given. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1314612
- author
- Carlehed, Magnus; Cegrell, Urban and Wikström, Frank ^{LU}
- publishing date
- 1999
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Annales Polonici Mathematici
- volume
- 71
- issue
- 1
- pages
- 87 - 103
- publisher
- Institute of Mathematics, Polish Academy of Sciences
- ISSN
- 1730-6272
- language
- English
- LU publication?
- no
- id
- ee3090b7-a73d-425a-bd24-bc09b681879e (old id 1314612)
- date added to LUP
- 2009-05-11 15:00:31
- date last changed
- 2017-01-13 13:29:06
@article{ee3090b7-a73d-425a-bd24-bc09b681879e, abstract = {Let <br/><br> be a bounded domain in CN. Let z be a point in <br/><br> and let Jz be the set of all Jensen<br/><br> measures on <br/><br> with barycenter at z with respect to the space of functions continuous on <br/><br> and<br/><br> plurisubharmonic in <br/><br> . The authors prove that <br/><br> is hyperconvex if and only if, for every z 2 @<br/><br> ,<br/><br> measures in Jz are supported by @<br/><br> . From this they deduce that a pluricomplex Green function<br/><br> g(z,w) with its pole at w continuously extends to @<br/><br> with zero boundary values if and only if <br/><br> <br/><br> is hyperconvex.<br/><br> Then the authors give a criterion for Reinhardt domains to be hyperconvex and explicitly compute<br/><br> the pluricomplex Green function on the Hartogs triangle.<br/><br> The last sections are devoted to the boundary behaviour of pluricomplex Green functions. Such<br/><br> a function has Property (P0) at a point w0 2 @<br/><br> if limw!w0 g(z,w) = 0 for every z 2 <br/><br> . If the<br/><br> convergence is uniform in z on compact subsets of <br/><br> r{w0}, then w0 has Property (P0). Several<br/><br> sufficient conditions for points on the boundary with these properties are given.}, author = {Carlehed, Magnus and Cegrell, Urban and Wikström, Frank}, issn = {1730-6272}, language = {eng}, number = {1}, pages = {87--103}, publisher = {Institute of Mathematics, Polish Academy of Sciences}, series = {Annales Polonici Mathematici}, title = {Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function}, volume = {71}, year = {1999}, }