3 citations · 14 across the 13 of their papers we have counts for
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Auxiliary Monge-Ampere equations in geometric analysis
Bin Guo, Duong H. Phong
This is an introduction to a particular class of auxiliary complex Monge-Ampère equations which had been instrumental in estimates for fully non-linear equations and var…
Diameter estimates in Kähler geometry
Bin Guo, Duong H. Phong, Jian Song +1
Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for $…
Green's functions and complex Monge-Ampère equations
Bin Guo, Duong H. Phong, Jacob Sturm
Uniform and lower bounds are obtained for the Green's function on compact Kähler manifolds. Unlike in the classic theorem of Cheng-Li for Riemannian manifolds, the lower boun…
On the Hessian-cscK equations
Bin Guo, Kevin Smith, Freid Tong
In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature Kähler (cscK) metrics. We show this system can…
Stability estimates for the complex Monge-Ampère and Hessian equations
Bin Guo, Duong H. Phong, Freid Tong
A new proof for stability estimates for the complex Monge-Ampère and Hessian equations is given, which does not require pluripotential theory. A major advantage is that the resulti…
A new gradient estimate for the complex Monge-Ampère equation
Bin Guo, Duong H. Phong, Freid Tong
A gradient estimate for complex Monge-Ampère equations which improves in some respects on known estimates is proved using the ABP maximum principle.