Complex analysis
On the regularization of J-plurisubharmonic functions
Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 17-19.

We show that on almost complex surfaces plurisubharmonic functions can be locally approximated by smooth plurisubharmonic functions. The main tool is the Poletsky type theorem due to U. Kuzman.

Nous montrons que, sur une surface presque complexe, les fonctions pluri-sous-harmo-niques peuvent étre localement approximées par des fonctions pluri-sous-harmoniques lisses. La méthode consiste à appliquer le théorème de type Polestsky démontré par U. Kuzman.

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DOI: 10.1016/j.crma.2014.11.001
Pliś, Szymon 1

1 Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland
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Pliś, Szymon. On the regularization of J-plurisubharmonic functions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 17-19. doi : 10.1016/j.crma.2014.11.001. http://www.numdam.org/articles/10.1016/j.crma.2014.11.001/

[1] Błocki, Z. On the definition of the Monge–Ampère operator in C2, Math. Ann., Volume 328 (2004), pp. 415-423

[2] Diederich, K.; Sukhov, A. Plurisubharmonic exhaustion functions and almost complex Stein structures, Michigan Math. J., Volume 56 (2008) no. 2, pp. 331-355

[3] Haggui, F. Fonctions FSH sur une variété presque complexe, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002) no. 6, pp. 509-514

[4] Harvey, R.; Lawson, B. Potential theory on almost complex manifolds, Ann. Inst. Fourier (Grenoble) (2014) (forthcoming) | arXiv

[5] R. Harvey, B. Lawson, S. Pliś, Smooth approximation of plurisubharmonic functions on almost complex manifolds, in preparation.

[6] Ivashkovich, S.; Rosay, J.-P. Schwarz-type lemmas for solutions of ¯-inequalities and complete hyperbolicity of almost complex manifolds, Ann. Inst. Fourier (Grenoble), Volume 54 (2004) no. 7, pp. 2387-2435

[7] Kuzman, U. Poletsky theory of discs in almost complex manifolds, Complex Var. Elliptic Equ., Volume 57 (2014) no. 2, pp. 262-270

[8] Pliś, S. Monge–Ampère operator on four dimensional almost complex manifolds | arXiv

[9] Poletsky, E. Plurisubharmonic functions as solutions of variational problems, Santa Cruz, CA, 1989 (Proc. Sympos. Pure Math.), Volume vol. 52, Amer. Math. Soc., Providence, RI (1991), pp. 163-171

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