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Rendiconti Lincei - Matematica e Applicazioni

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Volume 21, Issue 2, 2010, pp. 115–157
DOI: 10.4171/RLM/564

Published online: 2010-04-18

Jenkins−Strebel differentials

Enrico Arbarello[1] and Maurizio Cornalba[2]

(1) Università di Roma La Sapienza, Italy
(2) Università di Pavia, Italy

In this mostly expository paper we revisit a fundamental result of Strebel, asserting the existence and uniqueness, on Riemann surfaces of finite type, of Jenkins−Strebel differentials having double poles with prescribed ‘‘residues’’ at prescribed points. In particular, we give a selfcontained and somewhat shortened proof of Strebel’s result.

Keywords: Quadratic differentials, closed trajectories, Teichmüller space

Arbarello Enrico, Cornalba Maurizio: Jenkins−Strebel differentials. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), 115-157. doi: 10.4171/RLM/564