6 papers
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…
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 establis…
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…