On the Existence of Jenkins-strebel Differentials Using Harmonic Maps from Surfaces to Graphs
نویسنده
چکیده
We give a new proof of the existence ([HM], [Ren]) of a Jenkins-Strebel differential Φ on a Riemann surface R with prescribed heights of cylinders by considering the harmonic map from R 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 ([Mo]). §
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