5 papers · 1 filter
Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface
Zheng Huang
We study the canonical metric on a compact Riemann surface of genus at least two. While it is known that the canonical metric is of nonpositive curvature, we show that its Gaussian…
The Weil-Petersson Geometry On the Thick Part of the Moduli Space of Riemann Surfaces
Zheng Huang
On the thick part of the moduli space of Riemann surfaces, where there is a positive lower bound of the systole of the surface, we show that all Weil-Petersson Riemannian curvature…
Caculus of Variation and the -Bergman Metric on Teichmüller Space
Zheng Huang
The canonical metric on a Riemann surface is the pullback from the Euclidean metric on the Jacobian variety via the period map. We study its induced L^2 metric on Teichmuller space…
On Asymptotic Weil-Petersson Geometry of Teichmüller Space of Riemann Surfaces
Zheng Huang
In this paper, we study the asymptotic geometry of Teichmuller space of Riemann surfaces and give bounds on the Weil-Petersson sectional curvature of Teichmuller space, in terms of…
Asymptotic flatness of the Weil-Petersson metric on Teichmuller space
Zheng Huang
The sectional curvature of the Weil-Petersson metric on Teichmuller space is known to be negative. We show that this Weil-Petersson sectional curvature is not pinched from above by…