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Cegrell, Urban
Publications (10 of 21) Show all publications
Cegrell, U. (2019). Measures of finite pluricomplex energy. Annales Polonici Mathematici, 123(1), 203-213
Open this publication in new window or tab >>Measures of finite pluricomplex energy
2019 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, no 1, p. 203-213Article in journal (Refereed) Published
Abstract [en]

We study a complex Monge-Ampere type equation of the form (dd(c)u)(n) = ke(-u)dV/integral e(-u)dV.

Place, publisher, year, edition, pages
Institute of Mathemathics, Polish Academy of Sciences, 2019
Keywords
complex Monge-Ampere operator, Dirichlet's problem, plurisubharmonic function
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-165324 (URN)10.4064/ap180811-7-2 (DOI)000493728300012 ()
Available from: 2019-12-03 Created: 2019-12-03 Last updated: 2019-12-03Bibliographically approved
Åhag, P., Cegrell, U. & Hiep, P. H. (2019). On the Guedj-Rashkovskii conjecture. Annales Polonici Mathematici, 123(1), 15-20
Open this publication in new window or tab >>On the Guedj-Rashkovskii conjecture
2019 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, no 1, p. 15-20Article in journal (Refereed) Published
Abstract [en]

We prove some cases when the Guedj-Rashkovskii conjecture holds.

Place, publisher, year, edition, pages
Polish Academy of Sciences, 2019
Keywords
complex Monge-Ampere operator, Lelong number, plurisubharmonic function, the Guedj-Rashkovskii conjecture, the residual mass conjecture
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-165332 (URN)10.4064/ap180822-16-11 (DOI)000493728300003 ()
Available from: 2019-11-27 Created: 2019-11-27 Last updated: 2019-11-27Bibliographically approved
Åhag, P., Cegrell, U. & Phạm, H. H. (2015). Monge-Ampère measures on subvarieties. Journal of Mathematical Analysis and Applications, 423, 94-105
Open this publication in new window or tab >>Monge-Ampère measures on subvarieties
2015 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 423, p. 94-105Article in journal (Refereed) Published
Abstract [en]

In this article we address the question whether the complex Monge-Ampere equation is solvable for measures with large singular part. We prove that under some conditions there is no solution when the right-hand side is carried by a smooth subvariety in C-n of dimension k < n.

Keywords
Complex Monge-Ampere operator,  Dirichlet problem,  Pluripolar set,  Plurisubharmonic function
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-93533 (URN)10.1016/j.jmaa.2014.09.061 (DOI)000349706000008 ()
Available from: 2014-09-23 Created: 2014-09-23 Last updated: 2018-06-07Bibliographically approved
Åhag, P., Cegrell, U. & Czyz, R. (2015). Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge-Ampere operator. Journal of Mathematical Analysis and Applications, 422(2), 960-980
Open this publication in new window or tab >>Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge-Ampere operator
2015 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 422, no 2, p. 960-980Article in journal (Refereed) Published
Abstract [en]

In this paper we shall consider two types of vector ordering on the vector space of differences of negative plurisubharmonic functions, and the problem whether it is possible to construct supremum and infimum. Then we consider two different approaches to define the complex Monge-Ampere operator on these vector spaces, and we solve some Dirichlet problems. We end this paper by stating and discussing some open problems.

Keywords
Complex Monge-Ampere operator, Delta-plurisubharmonic function, Pluricomplex energy, urisubharmonic function, Vector ordering
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-98542 (URN)10.1016/j.jmaa.2014.09.022 (DOI)000344911800012 ()
Available from: 2015-01-30 Created: 2015-01-23 Last updated: 2018-06-07Bibliographically approved
Cegrell, U. (2012). Convergence in Capacity. Canadian mathematical bulletin, 55(2), 242-248
Open this publication in new window or tab >>Convergence in Capacity
2012 (English)In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 55, no 2, p. 242-248Article in journal (Refereed) Published
Abstract [en]

In this note we study the convergence of sequences of Monge-Ampere measures {(dd(c)u(s))(n)}, where {u(s)} is a given sequence of plurisubharmonic functions, converging in capacity.

National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-56982 (URN)10.4153/CMB-2011-078-6 (DOI)000304726300003 ()
Available from: 2012-07-03 Created: 2012-07-02 Last updated: 2018-06-08Bibliographically approved
Åhag, P., Cegrell, U. & Czyz, R. (2012). On Dirichlet's principle and problem. Mathematica Scandinavica, 110(2), 235-250
Open this publication in new window or tab >>On Dirichlet's principle and problem
2012 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 110, no 2, p. 235-250Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to give a new proof of the complete characterization of measures for which there exists a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite pluricomplex energy. The proof uses variational methods.

Place, publisher, year, edition, pages
Aarhus, Denmark: Matematiska inst. University of Munkegade, 2012
Keywords
monge-ampere operator, plurisubharmonic-functions, variational properties, pluricomplex energy, equation
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-45616 (URN)000306625600005 ()
Available from: 2011-08-03 Created: 2011-08-03 Last updated: 2018-06-08Bibliographically approved
Cegrell, U. (2012). Potentials with respect to the pluricomplex Green function. Annales Polonici Mathematici, 106, 107-111
Open this publication in new window or tab >>Potentials with respect to the pluricomplex Green function
2012 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, p. 107-111Article in journal (Refereed) Published
Abstract [en]

For μ a positive measure, we estimate the pluricomplex potential of μ, Pμ(x)=∫Ωg(x,y)dμ(y), where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.

Place, publisher, year, edition, pages
Institute of mathematics, Polish academy of sciences, 2012
Keywords
complex Monge-Ampere operator, energy classes, pluricomplex Green function, potential, plurisubharmonic function
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-104262 (URN)10.4064/ap106-0-8 (DOI)000311525700008 ()
Available from: 2015-06-10 Created: 2015-06-09 Last updated: 2018-06-07Bibliographically approved
Åhag, P., Cegrell, U. & Pham, H. H. (2010). A product property for the pluricomplex energy. Osaka Journal of Mathematics, 47(3), 637-650
Open this publication in new window or tab >>A product property for the pluricomplex energy
2010 (English)In: Osaka Journal of Mathematics, ISSN 0030-6126, Vol. 47, no 3, p. 637-650Article in journal (Refereed) Published
Abstract [en]

In this note we prove a product property for the pluricomplex energy, and then give some applications.

National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-36296 (URN)000285678700003 ()
Available from: 2010-09-27 Created: 2010-09-27 Last updated: 2018-06-08Bibliographically approved
Cegrell, U. (2009). Maximal plurisubharmonic functions. Uzbek Mathematical Journal (1), 10-16
Open this publication in new window or tab >>Maximal plurisubharmonic functions
2009 (English)In: Uzbek Mathematical Journal, no 1, p. 10-16Article in journal (Other academic) Published
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-25709 (URN)
Available from: 2009-08-31 Created: 2009-08-31 Last updated: 2018-06-08Bibliographically approved
Cegrell, U. & Kemppe, B. (2009). Monge-Ampère boundary measures. Annales Polonici Mathematici, 96(2), 175-196
Open this publication in new window or tab >>Monge-Ampère boundary measures
2009 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, no 2, p. 175-196Article in journal (Refereed) Published
Abstract [en]

We study swept-out Monge–Ampère measures of plurisubharmonic functions and boundary values related to those measures.

Identifiers
urn:nbn:se:umu:diva-19730 (URN)
Note
Tidigare version publicerad i rapportserie vid Institutionen för matematik och matematisk statistik, Umeå universitet: Research report in Mathematics (Umeå), ISSN: 1653-0810; 2007:6Available from: 2009-03-10 Created: 2009-03-10 Last updated: 2018-06-09
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