Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A comparison principle for bounded plurisubharmonic functions on complex varieties in $ \mathbb{C}^n$


Authors: Nguyen Quang Dieu and Sanphet Ounheuan
Journal: Proc. Amer. Math. Soc. 146 (2018), 309-323
MSC (2010): Primary 32U15; Secondary 32B15
DOI: https://doi.org/10.1090/proc/13735
Published electronically: August 1, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We establish a comparison principle for locally bounded plurisubharmonid functions on complex varieties (possibly with singularities) in bound-
ed domains in $ \mathbb{C}^n$.


References [Enhancements On Off] (What's this?)

  • [Be] Eric Bedford, The operator $ (dd^{c})^{n}$ on complex spaces, Seminar Pierre Lelong-Henri Skoda (Analysis), 1980/1981, and Colloquium at Wimereux, May 1981, Lecture Notes in Math., vol. 919, Springer, Berlin-New York, 1982, pp. 294-323. MR 658889
  • [BT1] Eric Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), no. 1-2, 1-40. MR 674165, https://doi.org/10.1007/BF02392348
  • [BT2] Eric Bedford and B. A. Taylor, Fine topology, Šilov boundary, and $ (dd^c)^n$, J. Funct. Anal. 72 (1987), no. 2, 225-251. MR 886812, https://doi.org/10.1016/0022-1236(87)90087-5
  • [BT3] Eric Bedford and B. A. Taylor, Uniqueness for the complex Monge-Ampère equation for functions of logarithmic growth, Indiana Univ. Math. J. 38 (1989), no. 2, 455-469. MR 997391, https://doi.org/10.1512/iumj.1989.38.38021
  • [Ce] Urban Cegrell, The general definition of the complex Monge-Ampère operator, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 1, 159-179 (English, with English and French summaries). MR 2069125
  • [Chi89] E. M. Chirka, Complex analytic sets, Mathematics and its Applications (Soviet Series), vol. 46, Kluwer Academic Publishers Group, Dordrecht, 1989. Translated from the Russian by R. A. M. Hoksbergen. MR 1111477
  • [FN] John Erik Fornæss and Raghavan Narasimhan, The Levi problem on complex spaces with singularities, Math. Ann. 248 (1980), no. 1, 47-72. MR 569410, https://doi.org/10.1007/BF01349254
  • [GH] Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1994. Reprint of the 1978 original. MR 1288523
  • [KH] Nguyen Van Khue and Pham Hoang Hiep, A comparison principle for the complex Monge-Ampère operator in Cegrell's classes and applications, Trans. Amer. Math. Soc. 361 (2009), no. 10, 5539-5554. MR 2515822, https://doi.org/10.1090/S0002-9947-09-04730-8
  • [Xi1] Yang Xing, Continuity of the complex Monge-Ampère operator, Proc. Amer. Math. Soc. 124 (1996), no. 2, 457-467. MR 1322940, https://doi.org/10.1090/S0002-9939-96-03316-3
  • [Xi2] Yang Xing, A strong comparison principle for plurisubharmonic functions with finite pluricomplex energy, Michigan Math. J. 56 (2008), no. 3, 563-581. MR 2490646, https://doi.org/10.1307/mmj/1231770360

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 32U15, 32B15

Retrieve articles in all journals with MSC (2010): 32U15, 32B15


Additional Information

Nguyen Quang Dieu
Affiliation: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy street, Cau Giay, Hanoi, Vietnam
Email: dieu$_$vn@yahoo.com

Sanphet Ounheuan
Affiliation: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy street, Cau Giay, Hanoi, Vietnam
Email: sanphetMA@gmail.com

DOI: https://doi.org/10.1090/proc/13735
Keywords: Plurisubharmonic functions, complex varieties, Monge-Amp\`ere operator
Received by editor(s): December 7, 2016
Received by editor(s) in revised form: March 5, 2017
Published electronically: August 1, 2017
Communicated by: Franc Forstneric
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society