12 citations · 45 across the 19 of their papers we have counts for
19 papers
Limits of Hyperkähler Manifolds and Moduli Spaces of Sheaves on K3 Surfaces
Kefeng Liu, Yang Shen
We prove that a compact strongly Gauduchon manifold which is a limit of compact hyperkähler manifolds is bimeromorphic to a compact hyperkähler manifold. This settles a case of a c…
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, we…
Sections of Hodge bundles I: Global theory and applications to period maps
Kefeng Liu, Yang Shen
We study global sections of Hodge bundles arising from two complementary constructions: a deformation-theoretic construction, which yields global geometric consequences for period…
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…
Penrose transformation on flag domains
Kefeng Liu, Yang Shen
Building on our recent work, we construct the Penrose transformations of the cohomology groups of homogeneous line bundles on flag domains , where is of Hermit…
Vanishing Theorems and Complex Structures on Non-Classical Flag Domains
Kefeng Liu, Yang Shen
Let be a non-classical flag domain with simple. We prove that every compact quotient of by a torsion-free discrete subgroup has no nonzero c…
Non-simple systoles on random hyperbolic surfaces for large genus
Yuxin He, Yang Shen, Yunhui Wu +1
In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface…
The Cheeger constants of random Belyi surfaces
Yang Shen, Yunhui Wu
Brooks and Makover developed a combinatorial model of random hyperbolic surfaces by gluing certain hyperbolic ideal triangles. In this paper we show that for any , as the numb…
Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps
Yang Shen, Yunhui Wu
Let be the moduli space of hyperbolic surfaces of genus with punctures endowed with the Weil-Petersson metric. In this paper we study the asymptot…
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 manifol…
Moduli spaces as ball quotients I, local theory
Kefeng Liu, Yang Shen
We give a Hodge theoretic criterion to characterize locally the period domains of certain projective manifolds to be complex balls.
Algebraicity of the image of period map
Kefeng Liu, Yang Shen
We prove that the image of period map is algebraic, as conjectured by Griffiths.
From local Torelli to global Torelli
Kefeng Liu, Yang Shen
We introduce the notions of strong local Torelli and T-class for polarized manifolds, and prove that strong local Torelli implies global Torelli theorem on the Torelli spaces for p…
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…
Applications of the affine structures on the Teichmüller spaces
Kefeng Liu, Yang Shen, Xiaojing Chen
We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of Calabi--Yau manifolds, a global splitting prop…
Hodge metric completion of the moduli space of Calabi-Yau manifolds
Kefeng Liu, Yang Shen
In this paper, it is proved that the Hodge metric completion of the moduli space of polarized and marked Calabi-Yau manifolds, i.e. the Torelli space, is a complex affine manifold.…
Global Torelli Theorem for Projective Manifolds of Calabi-Yau Type
Kefeng Liu, Yang Shen
We prove that the period maps from the Torelli space and the moduli space with level structure of Calabi-Yau type manifolds to the corresponding period domain of polarized Hodg…
A Global Torelli Theorem for Calabi-Yau Manifolds
Kefeng Liu, Yang Shen, Andrey Todorov
We describe the proof that the period map from the Torelli space of Calabi-Yau manifolds to the classifying space of polarized Hodge structures is an embedding. The proof is based…