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Uzbekistan Urgench
Year
2023
Volume
33
Issue
1
Pages
3-16
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Section Mathematics
Title Potential theory on an analytic surface
Author(-s) Abdullaev B.I.ab, Kamolov Kh.Q.b
Affiliations Institute of Mathematics, Khorezm Branch, Uzbekistan Academy of Sciencesa, Urgench State Universityb
Abstract The work is devoted to the theory of pluripotential on analytic surfaces. The pluripotential theory on the complex space ${\mathbb C}^{n},$ as well as on the Stein complex manifold $X\subset{\mathbb C}^{N}$ (without a singular set) have been studied in enough detail. In this work, we propose a new approach for studying the main objects of potential theory on an analytic set with a non-empty singular (critical) set.
Keywords analytic set, plurisubharmonic function, pluripolar set, ${\mathcal{P}}$-measure, maximal function
UDC 517.55, 517.57
MSC 32U05, 32U15
DOI 10.35634/vm230101
Received 4 October 2022
Language Russian
Citation Abdullaev B.I., Kamolov Kh.Q. Potential theory on an analytic surface, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 1, pp. 3-16.
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