Given any compact Riemann surface with finitely many punctures, we show that there exists a unique Jenkins–Strebel differential on the Riemann surface with prescribed heights. In addition, the differential has second order poles at the distinguished punctures with prescribed leading coefficients. As a corollary, we obtain the solution of the moduli problem.
Cite this article
Jinsong Liu, Jenkins–Strebel differentials with poles. Comment. Math. Helv. 83 (2008), no. 1, pp. 211–240DOI 10.4171/CMH/123