On Asymptotic Weil-Petersson Geometry of Teichmuller Space of Riemann Surfaces

We investigate the asymptotic behavior of curvatures of the Weil-Petersson metric in Teichm¨uller space. We use a pointwise curvature estimate to study directions, in the tangent space, of extremely negative curvature and directions of asymptotically zero curvatures.

Keywords

The Weil-Petersson metric, Curvature, Harmonic maps, Riemann surfaces

2010 Mathematics Subject Classification

30F60, 32G15

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Published 1 January 2007