Absorbent,parabolic, elliptic and quasielliptic balayages in potential theory; relationships with the Green function

In the frame of standard H-cones of functions (the cone of all excessive functions with respect to a submarkovian resolvent of kernels with reference measure on a measurable space) on a Green set we show that the cofine closure of the complement of an absorbent set in coabsorbent. We obtain different characterizations concerning the parabolicity, ellipticity and quasiellipticity in terms of the Green function. We also show that these notions are the same in the direct and the dual theory.