Some Global Solutions of the Complex Monge-Ampère Equation

• Autorzy: Czyż R.
• Języki publikacji: EN

Abstrakty

EN

We give some sufficient condition which guarantee that for given plurisubharmonic function u (satisfying this condition) one can solve the global Monge-Ampère equation in Cⁿ: (dd^cv)ⁿ = dμ, for any positive Borel measures dμ, which are "close" to Monge-Ampère measure of the function u.

Słowa kluczowe

EN

complex Monge-Ampère operator; plurisubharmonic functions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 3
• Strony: 287--296
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Czyż R.

• Department of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland,

Bibliografia

• [1] R. Czyż, The complex Monge-Ampère equation for complex homogeneous functions in Cn, Ann. Polon. Math., 76 (3) (2001) 287-302.
• [2] A. Jeune, Prescription de la courbure de Ricci sur Cn, n > 2, Bull. Sci. Math., 2e serie, 116 (1992) 185-226.
• [3] S. Kołodziej, The complex Monge-Ampère equations, Acta Math., 180 (1998) 67-117.
• [4] S. Kołodziej, Existence and regularity of global solutions to the complex Monge-Ampère equation, to be published.
• [5] M. Klimek, Pluripotential theory, Oxford University Press, New York 1991.
• [6] D. R. Monn, Regularity of the complex Monge-Ampère equation for the radially symmetric functions of the unit ball, Math. Ann., 275 (1986) 501-511.