Uniqueness Theorems for Subharmonic and Holomorphic Functions of Several   Variables on a Domain
  We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and restrictions on the growth of functions near the boundary of domain. 
Bulat Khabibullin, Nargiza Tamindarova
math.CV