Author

Kwok-Kun Kwong

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Preprint Sep 2026

Jacobian estimates and geometric inequalities under intermediate Ricci curvature

We prove a Jacobian estimate underlying both the Heintze--Karcher comparison and the Alexandrov--Bakelman--Pucci method for submanifolds of arbitrary codimension. The estimate retains the contributions of ambient curvature along geodesics emanating from the submanifold and requires no curvature sign assumption. As appl...

Kwok-Kun Kwong, JiHyeog Lee, Fabio Ricci · 0 citations

Preprint Aug 2026

An improved volume bound under Ricci and scalar curvature lower bounds

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 if a closed Riemannian manifold $(N^n, g)$ satisfies $\operatorname{Ric}_g\ge (n-1)g$ and the scalar curvature $R_g\ge n(n-1)(1+\varepsilon)$...

Kwok-Kun Kwong · 2 citations · ⚡1

Preprint Aug 2026

An improved volume bound under Ricci and scalar curvature lower bounds

We study volume comparison for closed Riemannian manifolds satisfying a positive Ricci curvature lower bound together with an improved scalar curvature lower bound. Using an integral extension of the finite shuffling comparison for scalar Jacobi solutions due to Brown and Freedman \cite{BrownFreedman2022}, we prove tha...

Kwok-Kun Kwong · 2 citations · ⚡1