Let R, S be noncompact Riemannian m-manifolds and let T:R—>S be a Dirichlet mapping. Consider a nonnegative locally bounded measurable m-iorm P on R and set Q—T*lP, the pull-back of P under r-1. Denote by PE(R) {QE(S) resp.) the space of energy-finite solutions of Au=Pu on R (Au = Qu on 5 resp.). The spaces PE(R) and QE(S) are isomorphic, the isomorphism being bicontinuous with respect to the energy norms and preserves the sup norm of bounded solutions. Let R, S be noncompact Riemannian w… Expand

1. Various strides have been done to characterize the conformal structure of Riemann surfaces by the algebraic structure of some appropriate function algebras on them (cf. Bers [2], Rudin [29],… Expand