6 papers
Maximal Normal Curvature and Veronese Rigidity
Tsz-Kiu Aaron Chow, Jingbo Wan
We prove a sharp Veronese rigidity theorem for closed immersed submanifolds of the Euclidean unit ball under intrinsic harmonic-structure assumptions. For an isometric immersion $F…
Sharp focal radius estimate and rigidity of hypersurfaces in manifolds with positive curvature
Tsz-Kiu Aaron Chow, Jingbo Wan
We prove a sharp Clifford-threshold focal-radius estimate and rigidity for immersed hypersurfaces. Under a -form curvature condition, formulated by the Weitzenböck curvature te…
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…
Rigidity results for initial data sets satisfying the dominant energy condition
Christian Baer, Simon Brendle, Tsz-Kiu Aaron Chow +1
Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energ…
Scalar curvature rigidity for products of spheres and tori
Tsz-Kiu Aaron Chow
We prove Llarull-type rigidity for (, ). If a closed spin admits a degree-nonzero map to $S^{n-m}\times\mathbb{T}^…
Bandwidth and focal radius with positive isotropic curvature
Tsz-Kiu Aaron Chow, Jingze Zhu
This paper investigates quantitative metric inequalities for manifolds with positive isotropic curvature (PIC). Our results include upper bounds on the bandwidth and focal radius o…