Harmonic manifolds with mimimal horospheres (Q1407747)

For a non-compact harmonic manifold \(M\), the authors present an integral formula for the derivative of a harmonic function on \(M\); as a consequence, they show that for harmonic spaces having minimal horospheres, bounded harmonic functions are constant. The authors also show that if the volume density function of \(M\) has polynomial growth, then \(M\) is flat. The authors further give sufficient conditions for polynomial growth of the volume function.