27 citations · 61 across the 30 of their papers we have counts for
34 papers
Higher order isoperimetric inequalities and rigidity for surfaces in
Xu-Qian Fan, Kwok-Kun Kwong
We establish a family of sharp higher order isoperimetric type inequalities for smooth compact surfaces in Euclidean spaces of arbitrary codimension. These inequalities involve arb…
Jacobian estimates and geometric inequalities under intermediate Ricci curvature
Kwok-Kun Kwong, Jihye Lee, Fabio Ricci
We prove a Jacobian estimate underlying both the Heintze--Karcher comparison and the Alexandrov--Bakelman--Pucci method for submanifolds of arbitrary codimension. The estimate reta…
An improved volume bound under Ricci and scalar curvature lower bounds
Kwok-Kun Kwong
We study volume comparison for closed Riemannian manifolds satisfying a positive Ricci curvature lower bound together with an improved scalar curvature lower bound. We prove that i…
Heintze-Karcher and Reverse Alexandrov-Fenchel Inequalities via Focal Geometry
Kwok-kun Kwong, Scott Parkins, Glen Wheeler
We prove a collection of reverse Alexandrov-Fenchel type inequalities in anisotropic, Euclidean, spherical, and hyperbolic settings. The unifying principle is that the relevant def…
Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifolds
Meng Ji, Kwok-Kun Kwong
In this paper, we uncover a novel connection between the Fenchel-Willmore inequality and a new logarithmic Sobolev inequality for mean-convex submanifolds immersed in non-negativel…
Fenchel-Willmore inequality for submanifolds in manifolds with non-negative -Ricci curvature
Meng Ji, Kwok-Kun Kwong
We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative interme…