The heat equation and harmonic maps of complete manifolds (Q1814170)

The authors study harmonic maps between complete noncompact manifolds. Their main goal is to obtain sufficient conditions (on the Ricci or sectional curvatures of the manifolds under consideration and sometimes on the spectrum of the initial manifold) under which a \(C^ 1\) map \(h\) of bounded energy density between two such manifolds can be deformed smoothly to a smooth harmonic map by solving the parabolic equation for harmonic maps.