Uma demonstração probabilística do teorema de Cheng-Liouville - Eduardo de Amorim Neves (2008)
The following theorem due to S.-Y.Cheng [6]: Let f: M → N be a harmonic map, where M and N are complete Riemannian manifolds. Suppose that M has nonnegative Ricci curvature, N has nonpositive sectional curvature, and N is simply connected. If f has sublinear asymptotic growth, then f must be a constant map. There is a probabilistic proof of this theorem due to the Seth Stafford [25]. The aim of this work is to reproduce this proof with details for the case N = Rn