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On Jenkins-Strebel differentials for open Riemann surfaces

Published online by Cambridge University Press:  14 November 2011

Frederick P. Gardiner
Frederick P. Gardiner
Affiliation:
Department of Mathematics, Brooklyn College, CUNY, New York, U.S.A.
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Synopsis

Dual extremum problems associated with an infinite family of admissible loops on a Riemann surface are shown to be solvable by Jenkins-Strebel differentials. Then the inequalities associated with these problems are used to calculate the first derivatives of extremal length functionals on Teichmüller space and to estimate the difference quotients for the second derivatives of these functions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 3-4 , 1980 , pp. 315 - 325
Copyright
Copyright © Royal Society of Edinburgh 1980

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References

1Ahlfors, L. V.. Conformai Invariants; Topics in Geometric Function Theory (New York: McGraw-Hill, 1973).Google Scholar
2Jenkins, J. A.. On the existence of certain general extremal metrics. Ann. Math. 66 (1957), 440–453.Google Scholar
3Oikawa, K.. A problem on the deformation and extension of Riemann surfaces, to appear.Google Scholar
4Strebel, K.. On quadratic differentials with closed trajectories on open Riemann surfaces, to appear.Google Scholar
5Wolpert, S.. The Weil-Petersson Metric for Teichmüller Space, Jenkins-Strebel Differentials (Thesis, Stanford Univ., 1976).Google Scholar