EQUIBOUNDEDNESS OF THE WEIL-PETERSSON METRIC

作者：Wolpert Scott A^*

来源：Transactions of the American Mathematical Society, 2017, 369(8): 5871-5887.

DOI：10.1090/tran/6998

Given a topological type for surfaces of negative Euler characteristic, uniform bounds are developed for derivatives of solutions of the 2dimensional constant negative curvature equation and the Weil-Petersson metric for the Teichmuller and moduli spaces. The dependence of the bounds on the geometry of the underlying Riemann surface is studied. The comparisons between the C-0, C-2,C-alpha and L-2 norms for harmonic Beltrami differentials are analyzed. Uniform bounds are given for the covariant derivatives of the WeilPetersson curvature tensor in terms of the systoles of the underlying Riemann surfaces and the projections of the differentiation directions onto pinching directions. The main analysis combines Schauder and potential theory estimates with the analytic implicit function theorem.

• 出版日期2017-8