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On the Existence of Jenkins-Strebel Differentials Using Harmonic Maps from Surfaces to Graphs

Michael Wolf
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Abstract

We give a new proof of the existence (\cite{HM}, \cite{Ren}) of a Jenkins-Strebel differential $Φ$ on a Riemann surface $\SR$ with prescribed heights of cylinders by considering the harmonic map from $\SR$ to the leaf space of the vertical foliation of $Φ$, thought of as a Riemannian graph. The novelty of the argument is that it is essentially Riemannian as well as elementary; moreover, the harmonic maps existence theory on which it relies is classical, due mostly to Morrey (\cite{Mo}).

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BibTeXRIS

Michael Wolf. 1994-06-29. On the Existence of Jenkins-Strebel Differentials Using Harmonic Maps from Surfaces to Graphs. https://arxiv.org/abs/dg-ga/9406003

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