Manifolds Carrying Bounded Quasiharmonic but No Bounded Harmonic Functions.

摘要

The main unsolved problem in the harmonic and quasiharmonic classification of Riemannian manifolds is the existence of manifolds carrying quasiharmonic functions with various boundedness properties but not carrying nonconstant harmonic functions with similar boundedness properties. Only a few scattered results have thus far been obtained in this direction. The present paper introduces a manifold which completely solves all these problems for dimension N > or = 3 and combines earlier results in one construction.