Abstract: In this talk, we show that the minimal length of a filling geodesic on a genus g hyperbolic surface in the surface moduli space is realized by the geodesic whose complement is a right-angled regular (8g-4)-gon, among the filling geodesics whose complements have at most one triangle or at most one non-triangle polygon, and a concrete example realizing this minimum is provided.
This is a joint work with Jiajun Wang and Zhongzi Wang.
