论文标题
谐波图的分解定理
A factorization theorem for harmonic maps
论文作者
论文摘要
让$ f $是从黎曼表面到riemannian $ n $ manifold的谐波地图。我们证明，如果表面的开放子集之间存在全体形态的差异性$ h $，以便$ f \ circ h = f $，则通过holomorthic Map通过holomorthic Map到另一个Riemann表面上。如果这样的$ h $是反塑形的，我们会获得类似的陈述。对于最小地图，该结果是众所周知的，是由于Gulliver-Osserman-Royden引起的分支浸入表面的理论的结果。我们的证明依赖于HOPF差异的各种几何特性。
Let $f$ be a harmonic map from a Riemann surface to a Riemannian $n$-manifold. We prove that if there is a holomorphic diffeomorphism $h$ between open subsets of the surface such that $f\circ h = f$, then $f$ factors through a holomorphic map onto another Riemann surface. If such $h$ is anti-holomorphic, we obtain an analogous statement. For minimal maps, this result is well known and is a consequence of the theory of branched immersions of surfaces due to Gulliver-Osserman-Royden. Our proof relies on various geometric properties of the Hopf differential.
