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Canonical Metrics on the Moduli Space of Riemann Surfaces II
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
In this paper we continue our study on the canonical metrics on the Teichmüller and the moduli space of Riemman surfaces. We first prove the equivalence of the Bergman metric and t…
Affine Manifolds, SYZ Geometry, and the "Y" Vertex
John Loftin, Shing-Tung Yau, Eric Zaslow
We study the real Monge-Ampère equation in two and three dimensions, both from the point of view of the SYZ conjecture, where solutions give rise to semi-flat Calabi-Yau's and in a…
Canonical Metrics on the Moduli Space of Riemann Surfaces I
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
We prove the equivalences of several classical complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new Kähler metrics, the Ricci met…