On the complex Monge-Ampère operator in unbounded domains
Wybierz format
RIS BIB ENDNOTEOn the complex Monge-Ampère operator in unbounded domains
Data publikacji: 24.11.2017
Universitatis Iagellonicae Acta Mathematica, 2017, Tom 54, s. 7-13
https://doi.org/10.4467/20843828AM.17.001.7077Autorzy
On the complex Monge-Ampère operator in unbounded domains
In this note we give sufficient conditions on a measure µ, defined on a unbounded strictly hyperconvex domain in Cn, to be the MongeAmpere measure of some plurisubharmonic function. These generalize recent results by Le et al.
1. Ahag P., Cegrell U., Czyz R., Ph¤m H. H., Monge–Ampère measures on pluripolar sets, J. Math. Pures Appl., 92 (2009), 613–627.
2. –Ahag P., Czyz R., Kolodziej's subsolution theorem for unbounded pseudoconvex domains, Univ. Iagel. Acta Math., 50 (2012), 7–23.
3. Blocki Z., Estimates for the complex Monge–Ampère operator, Bull. Pol. Acad. Sci. Math., 41 (1993), 151–157.
4. Cegrell U., The general definition of the complex Monge–Ampère operator, Ann. Inst. Fourier (Grenoble), 54 (2004), 159–179.
5. Cegrell U., A general Dirichlet problem for the complex Monge–Ampère operator, Ann. Polon. Math., 94 (2008), 131–147.
6. Cegrell U., Hed L., Subextension and approximation of negative plurisubharmonic functions, Michigan Math. J., 56 (2008), no. 3, 593–601.
7. Czyz R., The complex Monge–Ampère operator in the Cegrell classes, Dissertationes Math., 466 (2009), 83 pp.
8. Hed L., Approximation of negative plurisubharmonic functions with given boundary values, Internat. J. Math., 21 (2010), no. 9, 1135–1145.
9. Jarnicki M., Zwonek W., personal communication, Krakâw, Poland, 8th July 2011. 13
10. Le H. M., Nguy¹n H. X., Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications, Ann. Polon. Math., 112 (2014), no. 1, 55–66.
11. Le H. M., Nguy¹n H. X., Nguy¹n T. V., The complex Monge–Ampère equation in unbounded hyperconvex domains in Cn, Complex Var. Elliptic Equ., 59 (2014), no. 12, 1758–1774
12. Nguy¹n H. X., Monge–Ampère measures of maximal subextensions of plurisubharmonic functions with given boundary values, Complex Var. Elliptic Equ., 60 (2015), no. 3, 429–435.
13. Ph¤m H. H., Pluripolar sets and the subextension in Cegrell's classes, Complex Var. Elliptic Equ., 53 (2008), no. 7, 675–684.
Informacje: Universitatis Iagellonicae Acta Mathematica, 2017, Tom 54, s. 7-13
Typ artykułu: Oryginalny artykuł naukowy
Umea University Department of Mathematics and Mathematical Statistics Sweden
Instytut Matematyki, Uniwersytet Jagielloński, Kraków, Polska
Publikacja: 24.11.2017
Status artykułu: Otwarte
Licencja: CC BY-NC-ND
Udział procentowy autorów:
Korekty artykułu:
-Języki publikacji:
AngielskiLiczba wyświetleń: 2149
Liczba pobrań: 1590