Types of afforested surfaces

Abstract

We form, what we call, an afforested surface R over a plantation P by foresting with trees T_n (n $\in$ N: the set of positive integers). If all of P and T_n (n $\in$ N) belong to the class ${\mathscr O}_s$ of hyperbolic Riemann surfaces W carrying no singular harmonic functions on W, then we will show that, under a certain diminishing condition on roots of trees T_n (n $\in$ N), the afforested surface R also belongs to ${\mathscr O}_s$.