16 citations · 18 across the 9 of their papers we have counts for
7 papers · 1 filter
Fundamental groups of Calabi-Yau spaces
Xin Fu, Bin Guo, Jian Song +1
We study the fundamental groups of a normal projective Calabi-Yau variety with klt singularities and of its regular locus . We prove that both groups are almost abelia…
RCD structures on singular Kahler spaces of complex dimension three
Xin Fu, Bin Guo, Jian Song
Let X be a projective variety of complex dimension 3 with log terminal singularities. We prove that every singular Kahler metric on X with bounded Nash entropy and Ricci curvature…
Nash entropy, Calabi energy and geometric regularization of singular Kähler metrics
Bin Guo, Jian Song
We prove uniform Sobolev bounds for solutions of the Laplace equation on a general family of Kähler manifolds with bounded Nash entropy and Calabi energy. These estimates establish…
Diameter estimates in Kähler geometry II: removing the small degeneracy assumption
Bin Guo, Duong H. Phong, Jian Song +1
In this short note, we remove the small degeneracy assumption in our earlier works [10, 11]. This is achieved by a technical improvement of Corollary 5.1 in [10]. As a consequence,…
CscK metrics near the canonical class
Bin Guo, Wangjian Jian, Yalong Shi +1
Let be a Kähler manifold with semi-ample canonical bundle . It is proved by Jian-Shi-Song that for any Kähler class , there exists such that for all …
Sobolev inequalities on Kähler spaces
Bin Guo, Duong H. Phong, Jian Song +1
We establish a uniform Sobolev inequality for Kähler metrics, which only require an entropy bound and no lower bound on the Ricci curvature. We further extend our Sobolev inequalit…
Schauder estimates for equations with cone metrics, I
Bin Guo, Jian Song
This is the first paper in a series to develop a linear and nonlinear theory for elliptic and parabolic equations on Kähler varieties with mild singularities. Donaldson has establi…