The minimum of two plurisubharmonic functions and a new characterization of holomorphic functions

summary:We prove, among other results, that $\min (u,v)$ is plurisubharmonic (psh) when $u,v$ belong to a family of functions in ${\rm psh}(D)\cap \Lambda _{\alpha }(D),$ where $\Lambda _{\alpha }(D)$ is the $\alpha $-Lipchitz functional space with $1<\alpha