JournalscmhVol. 83 , No. 1DOI 10.4171/cmh/123

Jenkins–Strebel differentials with poles

  • Jinsong Liu

    Academy of Mathematics and System Sciences, Beijing, China
Jenkins–Strebel differentials with poles cover

Abstract

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.