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Cegrell, Urban

Open this publication in new window or tab >>Measures of finite pluricomplex energy### Cegrell, Urban

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_some",{id:"formSmash:j_idt191:0:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_otherAuthors",{id:"formSmash:j_idt191:0:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2019-12-03 Created: 2019-12-03 Last updated: 2019-12-03Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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

Open this publication in new window or tab >>On the Guedj-Rashkovskii conjecture### Åhag, Per

### Cegrell, Urban

### Hiep, Pham Hoang

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2019-11-27 Created: 2019-11-27 Last updated: 2019-11-27Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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

Open this publication in new window or tab >>Monge-Ampère measures on subvarieties### Åhag, Per

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Cegrell, Urban

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Phạm, Hoàng Hiệp

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_some",{id:"formSmash:j_idt191:2:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_otherAuthors",{id:"formSmash:j_idt191:2:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2014-09-23 Created: 2014-09-23 Last updated: 2018-06-07Bibliographically approved

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.

Open this publication in new window or tab >>Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge-Ampere operator### Åhag, Per

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Cegrell, Urban

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Czyz, Rafal

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_some",{id:"formSmash:j_idt191:3:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_otherAuthors",{id:"formSmash:j_idt191:3:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2015-01-30 Created: 2015-01-23 Last updated: 2018-06-07Bibliographically approved

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.

Open this publication in new window or tab >>Convergence in Capacity### Cegrell, Urban

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_some",{id:"formSmash:j_idt191:4:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_otherAuthors",{id:"formSmash:j_idt191:4:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_otherAuthors",multiple:true}); 2012 (English)In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 55, no 2, p. 242-248Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-56982 (URN)10.4153/CMB-2011-078-6 (DOI)000304726300003 ()
#####

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Available from: 2012-07-03 Created: 2012-07-02 Last updated: 2018-06-08Bibliographically approved

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.

Open this publication in new window or tab >>On Dirichlet's principle and problem### Åhag, Per

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Cegrell, Urban

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Czyz, Rafal

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_some",{id:"formSmash:j_idt191:5:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_otherAuthors",{id:"formSmash:j_idt191:5:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2011-08-03 Created: 2011-08-03 Last updated: 2018-06-08Bibliographically approved

Jagiellonian Univ, Inst Math, Krakow, Poland.

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.

Open this publication in new window or tab >>Potentials with respect to the pluricomplex Green function### Cegrell, Urban

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_some",{id:"formSmash:j_idt191:6:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_otherAuthors",{id:"formSmash:j_idt191:6:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_otherAuthors",multiple:true}); 2012 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, p. 107-111Article in journal (Refereed) Published
##### Abstract [en]

##### 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 ()
#####

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Available from: 2015-06-10 Created: 2015-06-09 Last updated: 2018-06-07Bibliographically approved

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.

Open this publication in new window or tab >>A product property for the pluricomplex energy### Åhag, Per

### Cegrell, Urban

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Pham, Hoang Hiep

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_some",{id:"formSmash:j_idt191:7:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_otherAuthors",{id:"formSmash:j_idt191:7:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_otherAuthors",multiple:true}); 2010 (English)In: Osaka Journal of Mathematics, ISSN 0030-6126, Vol. 47, no 3, p. 637-650Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-36296 (URN)000285678700003 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_j_idt366",{id:"formSmash:j_idt191:7:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_j_idt366",multiple:true});
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Available from: 2010-09-27 Created: 2010-09-27 Last updated: 2018-06-08Bibliographically approved

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

Open this publication in new window or tab >>Maximal plurisubharmonic functions### Cegrell, Urban

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_some",{id:"formSmash:j_idt191:8:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_otherAuthors",{id:"formSmash:j_idt191:8:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_otherAuthors",multiple:true}); 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)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_j_idt366",{id:"formSmash:j_idt191:8:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_j_idt366",multiple:true});
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Available from: 2009-08-31 Created: 2009-08-31 Last updated: 2018-06-08Bibliographically approved

Open this publication in new window or tab >>Monge-Ampère boundary measures### Cegrell, Urban

### Kemppe, Berit

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_some",{id:"formSmash:j_idt191:9:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_otherAuthors",{id:"formSmash:j_idt191:9:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_otherAuthors",multiple:true}); 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]

##### Identifiers

urn:nbn:se:umu:diva-19730 (URN)
#####

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##### 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

Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.

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