16 citations · 18 across the 9 of their papers we have counts for
11 papers
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…
Stability and gradient estimates for fully nonlinear elliptic equations on hermitian manifolds
Bin Guo, Jian Song
The known proofs of the gradient estimate for complex Hessian equations rely on the second order estimate of Hou-Ma-Wu and on a Liouville theorem of Dinew-Kolodziej. In this paper,…
Fundamental groups of compact Kahler varieties with nef anti canonical bundle
Xin Fu, Bin Guo, Jian Song +1
It is proved by M. Paun (1997, 2017) that the fundamental group of a compact Kahler manifold X is almost Abelian if the anti-canonical bundle -KX is nef. In this paper, we apply th…
Hölder estimates for degenerate complex Monge-Ampère equations
Bin Guo, Slawomir Kolodziej, Jian Song +1
Uniform and Hölder estimates were proved by the Kolodziej for complex Monge-Ampère equations on compact Kähler manifolds with volume measure with . On the oth…
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,…
Sup-slopes and sub-solutions for fully nonlinear elliptic equations
Bin Guo, Jian Song
We establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on closed Riemannian or hermitian manifolds, including both hess…
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…