Types of afforested surfaces

抄録

We form, what we call, an afforested surface R over a plantation P by foresting with trees T_n (n ∈ N: the set of positive integers). If all of P and T_n (n ∈ N) belong to the class ${¥mathcal O}_s$ 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 ∈ N), the afforested surface R also belongs to ${¥mathcal O}_s$.