On harmonic mappings of decreasing volume. (Chinese. English summary) Zbl 0595.58008
Summary: Assume that \(f: M\to N\) is a smooth mapping where M and N are Riemannian manifolds of dimensions m and n respectively. The mapping f is said to be volume decreasing if the \(\sigma_ m\)-energy density of f is not more than one everywhere. In this paper, we obtain three propositions about volume decreasing.
MSC:
58E20 | Harmonic maps, etc. |