Abstract
A formula for the sectional curvature of Teichmuller space with respect to the Weil-Petersson metric is derived in terms of the Laplace-Beltrami operator on functions. It will be shown that the sectional curvature as well as the holomorphic sectional curvature and Ricci curvature are negative. Bounds on the holomorphic and the Ricci curvature are given.
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