The representative theorem of a class of harmonic functions on Riemannian manifolds (Q1200049)

Given a complete noncompact Riemannian manifold \(M\), the author shows that a harmonic function \(u\) on \(M\times\mathbb{R}^ +\) satisfying \(\sup_{t>0}\| u(x,t)\|_{L^ p(M)}<\infty\) is the Poisson integral of some function. (For \(p=1,\infty\) an assumption on the Ricci curvature is required.) The result generalizes the classical theorem for \(M=\mathbb{R}^ m\).