119 citations · 119 across the 12 of their papers we have counts for
17 papers
Rigidity and flexibility under positive isotropic curvature
Tsz-Kiu Aaron Chow, Yipeng Wang
For every and , we construct a smooth -PIC metric on with Urysohn -width at least and an embedded stable minimal disk of intrinsic inradius at least $L…
Nonexistence of complete metrics with uniformly positive scalar curvature
Tsz-Kiu Aaron Chow
Let be a connected oriented even-dimensional manifold whose universal cover is spin. We prove that admits no complete metric with uniformly positive scalar curvature when e…
Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature
Tsz-Kiu Aaron Chow, Yipeng Wang
We improve the Micallef--Moore index estimate for harmonic two-spheres in -manifolds with positive isotropic curvature to the sharp bound . Combining with recent work, this…
Small Normal Curvature and Three-Manifold Topology
Tsz-Kiu Aaron Chow, Jingbo Wan
For , we prove that every smooth immersion satisfies , with equality only for the V…
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 ter…
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…
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…
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…
Preserving positive intermediate curvature
Tsz-Kiu Aaron Chow, Florian Johne, Jingbo Wan
Consider a compact manifold (with or without boundary) of dimension . Positive -intermediate curvature interpolates between positive Ricci curvature () and positiv…
Equivariant -manifolds with positive scalar curvature
Tsz-Kiu Aaron Chow, Yangyang Li
In this paper, for any compact Lie group , we show that the space of -invariant Riemannian metrics with positive scalar curvature (PSC) on any closed three-manifold is either…
Area and boundary length of surfaces diffeomorphic to annuli
Tsz-Kiu Aaron Chow
In this paper, we give a proof to a statement in Perelman's paper for finite extinction time of Ricci flow. Our proof draws on different techniques from the one given in Morgan-Tia…
Ricci Flow on Manifolds with Boundary with Arbitrary Initial Metric
Tsz-Kiu Aaron Chow
In this paper, we study the Ricci flow on manifolds with boundary. In the first part of the paper, we prove short-time existence and uniqueness of the solution, in which the bounda…
Positivity of Curvature on Manifolds with Boundary
Tsz-Kiu Aaron Chow
Consider a compact manifold with smooth boundary . Suppose that and are two Riemannian metrics on . We construct a family of metrics on which…
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…
Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapor cell
Chi Shu, Peng Chen, Tsz Kiu Aaron Chow +4
We report the efficient generation of subnatural-linewidth (< 6 MHz, for Rb D1/D2 lines) biphotons from a Doppler-broadened (530 MHz) hot atomic vapor cell. We use on-resonance spo…