3 citations · 4 across the 5 of their papers we have counts for
9 papers · 1 filter
A free boundary Monge-Ampère equation and applications to complete Calabi-Yau metrics
Tristan C. Collins, Freid Tong, Shing-Tung Yau
Let be a convex body containing the origin in its interior. We study a real Monge-Ampère equation with singularities along $\del P$ which is Legendre dual to a certain free bou…
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.
On estimates for complex Monge-Ampère equations
Bin Guo, Duong H. Phong, Freid Tong
A PDE proof is provided for the sharp estimates for the complex Monge-Ampère equation which had required pluripotential theory before. The proof covers both cases of fix…
On the degeneration of asymptotically conical Calabi-Yau metrics
Tristan C. Collins, Bin Guo, Freid Tong
We study the degenerations of asymptotically conical Ricci-flat Kähler metrics as the Kähler class degenerates to a semi-positive class. We show that under appropriate assumptions,…