Vol. 61, No. 2, 1975

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Noncompleteness of the Weil-Petersson metric for Teichmüller space

Scott Andrew Wolpert

Vol. 61 (1975), No. 2, 573–577

Let Tg be the Teichmüller space of a compact Riemann surface R of genus g with g 2. In the present paper it is shown that the Weil-Petersson Iength of a large class of rays is finite, deduced that the metric is not complete and indicated how the proof can be extended to the Teichmüller space of an arbitrary finitely generated Fuchsian group of the first kind. The proof is carried out by estimating the Weil-Petersson length of Teichmüller geodesic rays in directions corresponding to a certain class of quadratic differentials.

Mathematical Subject Classification 2000
Primary: 32G15
Secondary: 30A58
Received: 2 September 1975
Revised: 30 October 1975
Published: 1 December 1975
Scott Andrew Wolpert