10 papers
Nearly optimal spectral gaps for random Belyi surfaces
Yang Shen, Yunhui Wu
In this paper, we show that a random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than for some universal c…
Degenerations and Stability of Kähler Structures on Calabi--Yau Manifolds
Kefeng Liu, Yang Shen
In this paper, we study the degeneration and stability of Kähler structures on Calabi--Yau manifolds, namely compact Kähler manifolds with trivial canonical bundles, from the vie…
Simultaneous normalization of period map and affine structures on moduli spaces
Kefeng Liu, Yang Shen
We prove that the image of the lifted period map on the universal cover lies in a complex Euclidean space. We also prove that the Teichmüller spaces of a class of polarized manifo…
Boundedness of the images of period maps and applications
Kefeng Liu, Yang Shen
We prove a conjecture of Griffiths on simultaneous normalization of all periods which asserts that the image of the lifted period map on the universal cover lies in a bounded domai…
Boundedness of the Images of Period Maps
Kefeng Liu, Yang Shen
We prove a conjecture of Griffiths on simultaneous normalization of all periods which asserts that the image of the lifted period map on the universal cover lies in a bounded domai…
Sections of Hodge bundles II: Deformation of -classes and applications to Kähler geometry
Kefeng Liu, Yang Shen
Let be a compact Kähler manifold and its Kuranishi family, where may be singular and $\dim_{\C}B\ge1$. Using explicit sections of Hodge bundles, w…