Abstract
The Riemannian manifold D α {D_\alpha } obtained from the unit disk D by giving the distorted metric ( 1 − | z | ) − α | d z | {(1 - |z|)^{ - \alpha }}|dz| does not admit any Dirichlet finite nonharmonic biharmonic function if and only if α ≧ 3 4 \alpha \geqq \tfrac {3}{4} .
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