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

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

1994-06-29

arxiv.org/abs/dg-ga/9406003v1

Mathematics

Differential Geometry

8 pages, 2 figures available upon request

Scientific paper

We give a new proof of the existence (\cite{HM}, \cite{Ren}) of a Jenkins-Strebel differential $\Phi$ 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 $\Phi$, 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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