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arXiv · 2009.08377

A factorization theorem for harmonic maps

Nathaniel Sagman
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Abstract

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.

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Nathaniel Sagman. 2020-09-17. A factorization theorem for harmonic maps. https://arxiv.org/abs/2009.08377

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