Liouville theorems for self-similar solutions of heat flows
Liouville theorems for self-similar solutions of heat flows
Let N be a compact Riemannian manifold. A quasi-harmonic sphere is a harmonic map from ({\bf R}^m, e^{-|x|^2/2(m-2)}ds_0^2) to N ( m\geq 3 ) with finite energy ([LnW]). Here ds_0^2 is the Euclidean metric in {\bf R}^m . It arises from the blow-up analysis of the heat flow at a …