Uniqueness properties of m-subharmonic functions in Cegrell classes

The aim of the paper "Uniqueness properties of m-subharmonic functions in Cegrell classes" is to provide sufficient conditions for unicity of m-subharmonic functions. Since two plurisubharmonic functions may equal on an open subset of a domain without being identical (e.g. u ≡ 0 and v(z) = max(log |z|, 0)), it seems natural to put additional assumptions on Hessian measures of u and v to guarantee that u ≡ v on the whole domain Ω. The first result in this direction is the following remarkable theorem of Bloom and Levenberg about uniqueness of continuation of maximal plurisubharmonic functions. This theorem also found applications in some problems of weighted pluripotential theory.