3 citations · 10 across the 11 of their papers we have counts for
12 papers
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…
Generalized Monge-Ampère functionals and related variational problems
Freid Tong, Shing-Tung Yau
In this paper, we introduce a family of real Monge-Ampère functionals and study their variational properties. We prove a Sobolev type inequality for these functionals and use this…
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…
On estimates for Monge-Ampère and Hessian equations on nef classes
Bin Guo, Duong H. Phong, Freid Tong +1
The PDE approach developed earlier by the first three authors for estimates for fully non-linear equations on Kähler manifolds is shown to apply as well to Monge-Ampère…
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,…
A new positivity condition for the curvature of Hermitian manifolds
Freid Tong
In this note, we introduce a new type of positivity condition for the curvature of a Hermitian manifold, which generalizes the notion of nonnegative quadratic orthogonal bisectiona…
Longtime existence of Kähler Ricci flow and holomorphic sectional curvature
Shaochuang Huang, Man-Chun Lee, Luen-Fai Tam +1
In this work, we obtain a existence criteria for the longtime Kähler Ricci flow solution. Using the existence result, we generalize a result by Wu-Yau on the existence of Kähler Ei…
The Kähler-Ricci flow on manifolds with negative holomorphic curvature
Freid Tong
We study the behaviour of the normalized Kähler-Ricci flow on complete Kähler manifolds of negative holomorphic sectional curvature. We show that the flow exists for all time and c…