It is proved that any subharmonic function in a domain Ω ⊂ ℂⁿ which is plurisubharmonic outside of a real hypersurface of class C¹ is indeed plurisubharmonic in Ω.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-8, author = {E. M. Chirka}, title = {On the removal of subharmonic singularities of plurisubharmonic functions}, journal = {Annales Polonici Mathematici}, volume = {81}, year = {2003}, pages = {113-116}, zbl = {1026.32064}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-8} }
E. M. Chirka. On the removal of subharmonic singularities of plurisubharmonic functions. Annales Polonici Mathematici, Tome 81 (2003) pp. 113-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-8/