【摘要】
This talk is on recent progress on shortest filling geodesics on hyperbolic surfaces. A sharp lower bound of the length of filling geodesics is obtained. Moreover, we get a single filling geodesic on a hyperbolic surface realizing this lower bound.
For random hyperbolic surfaces, we show that the shortest filling geodesic length is asymptotic to g, in three random surface models: Weil-Petersson model, Brooks-Markover model, and random cover model. In the Weil-Petersson model, the $L^p$ norm of the shortest filling geodesic length is also calculated.
This talk is based on two pieces of joint work with Jiajun Wang, Zhongzi Wang and with Zhongzi Wang, Yunhui Wu respectively.
