45 citations · 85 across the 12 of their papers we have counts for
17 papers
Gromov-Hausdorff Convergence of Constant Scalar Curvature Kähler Metrics near the Canonical Class
Frederick Tsz-Ho Fong, Junbang Liu
Let be a compact Kähler manifold with semi-ample canonical bundle. For any Kähler class , Jian--Shi--Song proved that there exists a unique cscK metric in the class $2πc_1…
Singularity Models of Finite-Time Kähler-Ricci Flows
Frederick Tsz-Ho Fong, Hung Tran
We study the singularity type and models of the Kähler--Ricci flow on compact manifolds constructed from the 1-parameter foliation of a circle-bundle over a product of Kähler--Eins…
Ricci Flow on CP1-bundles over a Product of Kähler-Einstein Manifolds
Frederick Tsz-Ho Fong, Hung Tran
In this paper, we study the Ricci flow on CP1-bundles over a product of Kähler-Einstein manifolds whose initial metric is constructed by the ansatz used in works by M. Wang et. al.…
A Spinorial Perelman's Functional: Critical Points and Gradient Flow
Tsz-Kiu Aaron Chow, Frederick Tsz-Ho Fong
In this article, we introduce an energy functional on closed Riemannian spin manifolds which unifies Perelman's W- and F-functionals, Baldauf-Ouzch's E-functional, and Dirchlet ene…
Uniqueness and Symmetry of Self-Similar Solutions of Curvature Flows in Warped Product Spaces
Frederick Tsz-Ho Fong
In this article, we establish some uniqueness and symmetry results of self-similar solutions to curvature flows by some homogeneous speed functions of principal curvatures in some…
Higher-Order Estimates of Long-Time Solutions to the Kähler-Ricci Flow
Frederick Tsz-Ho Fong, Man-Chun Lee
In this article, we study the higher-order regularity of the Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. We proved, using a parabolic analo…
Local curvature estimates of long-time solutions to the Kähler-Ricci flow
Frederick Tsz-Ho Fong, Yashan Zhang
We study the local curvature estimates of long-time solutions to the normalized Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundles. Using these es…
Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows
Nicholas Cheng-Hoong Chin, Frederick Tsz-Ho Fong, Jingbo Wan
It has been known in that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows by degree -1 homogene…
Self-Expanders to Inverse Curvature Flows by Homogeneous Functions
Tsz-Kiu Aaron Chow, Ka-Wing Chow, Frederick Tsz-Ho Fong
In this paper, we study self-expanding solutions to a large class of parabolic inverse curvature flows by homogeneous symmetric functions of principal curvatures in Euclidean space…
Rotational Symmetry of Asymptotically Conical Mean Curvature Flow Self-Expanders
Frederick Tsz-Ho Fong, Peter McGrath
In this article, we examine complete, mean-convex self-expanders for the mean curvature flow whose ends have decaying principal curvatures. We prove a Liouville-type theorem associ…
Rotational symmetry of self-expanders to the inverse mean curvature flow with cylindrical ends
Gregory Drugan, Frederick Tsz-Ho Fong, Hojoo Lee
We show that any complete, immersed self-expander to the inverse mean curvature flow, which has one end asymptotic to a cylinder, or has two ends asymptotic to two coaxial cylinder…
Boltzmann's Entropy and Kähler-Ricci Solitons
Frederick Tsz-Ho Fong
We study a Boltzmann's type entropy functional (which appeared in existing literature) defined on Kähler metrics of a fixed Kähler class. The critical points of this functional are…
On 4-Dimensional J-Invariant Shrinking Ricci Solitons
Frederick Tsz-Ho Fong
As of today, there are very few known complete shrinking Ricci solitons in dimension 4, and all examples discovered so far are Kähler and/or Einstein. In this note, we prove that a…
Rotational Symmetry of Conical Kähler-Ricci Solitons
Otis Chodosh, Frederick Tsz-Ho Fong
We show that expanding Kähler-Ricci solitons which have positive holomorphic bisectional curvature and are asymptotic to Kähler cones at infinity must be the U(n)-rotationally symm…
The Collapsing Rate of the Kähler-Ricci Flow with Regular Infinite Time Singularity
Frederick Tsz-Ho Fong, Zhou Zhang
We study the collapsing behavior of the Kaehler-Ricci flow on a compact Kaehler manifold X admitting a holomorphic submersion X -> S coming from its canonical class, where S is a K…
On the collapsing rate of the Kähler-Ricci flow with finite-time singularity
Frederick Tsz-Ho Fong
This short note studies the collapsing behavior of the Kähler-Ricci flow on a compact Kähler manifold X admitting a holomorphic submersion X -> B where B is a Kähler manifold of lo…
Kähler-Ricci Flow on Projective Bundles over Kähler-Einstein Manifolds
Frederick Tsz-Ho Fong
We study the Kähler-Ricci flow on a class of projective bundles over compact Kähler-Einstein manifold . Assuming the initial Kähler metric…