4 citations · 9 across the 8 of their papers we have counts for
8 papers
On the modulus of continuity of solutions to complex Monge-Ampère equations
Bin Guo, Duong H. Phong, Freid Tong +1
In this paper, we prove a uniform and sharp estimate for the modulus of continuity of solutions to complex Monge-Ampère equations, using the PDE-based approach developed by the fir…
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.
Partial Legendre transforms of non-linear equations
Pengfei Guan, D. H. Phong
The partial Legendre transform of a non-linear elliptic differential equation is shown to be another non-linear elliptic differential equation. In particular, the partial Legendre…
A maximum rank problem for degenerate elliptic fully nonlinear equations
Pengfei Guan, D. H. Phong
The solutions to the Dirichlet problem for two degenerate elliptic fully nonlinear equations in dimensions, namely the real Monge-Ampère equation and the Donaldson equation,…
Regularity of geodesic rays and Monge-Ampere equations
D. H. Phong, Jacob Sturm
It is shown that the geodesic rays constructed as limits of Bergman geodesics from a test configuration are always of class . An essential step is to establish that…
On the scaling limit of a singular integral operator
I. M. Krichever, D. H. Phong
The scaling limit and Schauder bounds are derived for a singular integral operator arising from a difference equation approach to monodromy problems.