In this note, we introduce a class of maximal plurisubharmonic functions and use that class to prove some properties of maximal plurisubharmonics functions.
Dans cette note, nous introduisons une classe de fonctions pluri-sous-harmoniques maximales et utilisons celle-ci pour prouver certaines propriétés des fonctions pluri-sous-harmoniques maximales.
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@article{CRMATH_2019__357_11-12_858_0, author = {Do, Hoang-Son}, title = {A class of maximal plurisubharmonic functions}, journal = {Comptes Rendus. Math\'ematique}, pages = {858--862}, publisher = {Elsevier}, volume = {357}, number = {11-12}, year = {2019}, doi = {10.1016/j.crma.2019.11.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2019.11.003/} }
TY - JOUR AU - Do, Hoang-Son TI - A class of maximal plurisubharmonic functions JO - Comptes Rendus. Mathématique PY - 2019 SP - 858 EP - 862 VL - 357 IS - 11-12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2019.11.003/ DO - 10.1016/j.crma.2019.11.003 LA - en ID - CRMATH_2019__357_11-12_858_0 ER -
Do, Hoang-Son. A class of maximal plurisubharmonic functions. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 858-862. doi : 10.1016/j.crma.2019.11.003. http://archive.numdam.org/articles/10.1016/j.crma.2019.11.003/
[1] A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982) no. 1–2, pp. 1-40
[2] Survey of pluri-potential theory, Stockholm, 1987/1988 (Math. Notes), Volume vol. 38, Princeton University Press, Princeton, NJ, USA (1993), pp. 48-97
[3] The domain of definition of the complex Monge–Ampère operator, Amer. J. Math., Volume 128 (2006) no. 2, pp. 519-530
[4] Remark on the definition of the complex Monge–Ampère operator, Functional Analysis and Complex Analysis, Contemp. Math., vol. 481, Amer. Math. Soc., Providence, RI, USA, 2009, pp. 17-21
[5] The general definition of the complex Monge–Ampère operator, Ann. Inst. Fourier (Grenoble), Volume 54 (2004) no. 1, pp. 159-179 (in English, with French summary)
[6] Pluripotential Theory, Oxford University Press, Oxford, UK, 1991
[7] Maximal plurisubharmonic functions associated with holomorphic mappings, Indiana Univ. Math. J., Volume 47 (1998) no. 1, pp. 297-309
[8] Plurisubharmonic measures and capacities on complex manifolds, Russ. Math. Surv., Volume 36 (1981), pp. 61-119
[9] Continuity of envelopes of plurisubharmonic functions, J. Math. Mech., Volume 18 (1968), pp. 143-148
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☆ The author was funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2017.306.