Continuity of Subharmonic Functions
We prove that the set of points where a subharmonic function fails to be continuous is polar.
math.CV↗
arXiv subjects
Mansour Kalantar
Publications and source records attributed to Mansour Kalantar.
Family of Subharmonic Functions and Separately Subharmonic Functions
We prove that the upper envelope of a family of subharmonic functions defined on an open subset of $\mathbb{R}^{N}$, $(N\geq2)$, that is finite every where, is locally bounded above outside a closed nowhere dense set with no bounded components. Then we conclude as a consequence that a separately subharmonic function is subharmonic outside a closed nowhere dense set with no bounded components. It generalizes a result due to Cegrell and Sadullaev.
math.CV↗
Some Remarks on Quasinearly Subharmonic Functions
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
math.CV↗
Separately Subharmonic and Harmonic Functions are Subharmonic
We will prove that a function u(x,y) defined on a domain of RpxRq that is subharmonic in one variable and harmonic in the other is (jointly) subharmonic. This solves a long-standing open problem.
math.CV↗