Local Property of a Class of m-Subharmonic Functions
- 53 Downloads
In the paper, we introduce a new class of m-subharmonic functions with finite weighted complex m-Hessian. We prove that this class has local property.
Keywordsm-Subharmonic functions Weighted energy classes of m-subharmonic functions Complex m-Hessian Local property
Mathematics Subject Classification (2010)32U05 32U15 32U40 32W20
The paper was done while the author was visiting to Vietnam Institute for Advanced Study in Mathematics (VIASM) from May to June 2013. The author would like to thank the VIASM for hospitality and support. The author would like to thank Prof. Le Mau Hai for useful discussions which led to the improvement of the exposition of the paper. The author is also indebted to the referees for their useful comments that led to improvements in the exposition of the paper.
- 4.Benelkourchi, S., Guedj, V., Zeriahi, A.: Plurisubharmonic functions with weak singularities. In: Passare, M. (ed.) Complex Analysis and Digital Geometry: Proceedings from the Kiselmanfest, pp 57–73. Uppsala Universitet (2007)Google Scholar
- 6.Błocki, Z.: The Complex Monge–Ampere Operator in Pluripotential Theory. Lectures Notes (unpublished) (1998). http://gamma.im.uj.edu.pl/~blocki/publ/ln/wykl.pdf
- 12.Chinh, L.H.: On Cegrell’s classes of m-subharmonic functions. arXiv:1301.6502v1 (2013)
- 16.Hörmander, L.: Notions of convexity. Progress in Mathematics, vol. 127. Birkhäuser, Boston (1994)Google Scholar
- 20.Kołodziej, S.: The Complex Monge–Ampère Equation and Pluripotential Theory. Memoirs of the American Mathematical Society, vol. 178. American Mathematical Society, RI (2005)Google Scholar