Topology Seminar——Systole functions and Weil-Petersson geometry
报告人：Yunhui Wu (Tsinghua University)
时间：2019-10-24 14:30-16:30
地点：Room 1114, Sciences Building No. 1
Abstract:
The gradients of geodesic-length functions along systolic curves are studied. We show that the $L^p (1\leq p \leq \infty)$-norms of them at every closed hyperbolic surface $X$ are uniformly comparable to (systole(X))^{1/p}. Several applications to the Weil-Petersson geometry are discussed. For examples: (1). we reprove that the square root of the systole function is uniformly Lipschitz on the Teichmuller space endowed with the Weil-Petersson metric; (2). we also show that the minimal Weil-Petersson holomorphic sectional curvature at any closed hyperbolic surface is bounded above by a uniform negative constant independent of genus.
