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Comptes Rendus Mathématique
Volume 353, n° 1
pages 17-19 (janvier 2015)
Doi : 10.1016/j.crma.2014.11.001
Received : 26 September 2014 ;  accepted : 3 November 2014
On the regularization of J -plurisubharmonic functions
Sur la régularisation des fonctions J -pluri-sous-harmoniques

Szymon Pliś 1
 Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland 


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.

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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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1  The author was partially supported by the NCN grant 2011/01/D/ST1/04192.
2  In this note by the dimension of an almost complex manifold we mean the complex dimension which is a half of the real dimension.
3  “A function u is strictly plurisubharmonic on D ” means as usually that for any   there is   such that   is plurisubharmonic. We write here J -plurisubharmonic instead of plurisubharmonic to stress that a function is plurisubharmonic with respect to the almost complex structure J (note that on D we have also the almost complex structure  ).
4  Such domain D is called a Stain domain, see [[2]]. Here we can take   and   for   small enough.

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