187 citations · 2.2k across the 79 of their papers we have counts for
79 papers
Uniform estimates: subsolutions to fully nonlinear partial differential equations
Bin Guo, Duong H. Phong
Uniform bounds are obtained using the auxiliary Monge-Ampère equation method for solutions of very general classes of fully non-linear partial differential equations, assuming the…
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…
Geometric flows from unified string theories
Duong H. Phong
A survey of new geometric flows motivated by string theories is provided. Their settings can range from complex geometry to almost-complex geometry to symplectic geometry. From the…
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…
Uniform entropy and energy bounds for fully non-linear equations
Bin Guo, Duong H. Phong
Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Ampère equations invol…
On estimates for fully nonlinear partial differential equations
Bin Guo, Duong H. Phong
Sharp estimates are obtained for general classes of fully non-linear PDE's on non-Kähler manifolds, complementing the theory developed earlier by the authors in joint wo…