Tsz-Kiu Aaron Chow

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20172026

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16 papers · 1 filter

math.DG2026

Rigidity and flexibility under positive isotropic curvature

Tsz-Kiu Aaron Chow, Yipeng Wang

For every $n \geq 4$ and $L > 0$ , we construct a smooth $4$ -PIC metric on $S^{n}$ with Urysohn $1$ -width at least $L$ and an embedded stable minimal disk of intrinsic inradius at least $L…

math.DG2026

Nonexistence of complete metrics with uniformly positive scalar curvature

Tsz-Kiu Aaron Chow

Let $X$ be a connected oriented even-dimensional manifold whose universal cover is spin. We prove that $X$ admits no complete metric with uniformly positive scalar curvature when e…

math.DG2026

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 $n$ -manifolds with positive isotropic curvature to the sharp bound $n - 3$ . Combining with recent work, this…

math.DG2026

Small Normal Curvature and Three-Manifold Topology

Tsz-Kiu Aaron Chow, Jingbo Wan

For $m = 2, 3$ , we prove that every smooth immersion $F : R P^{m} ↬ B^{, N} (1)$ satisfies $κ (F)^{2} \geq 2 m / (m + 1)$ , with equality only for the V…

math.DG2026

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…

math.DG2026

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 $p$ -form curvature condition, formulated by the Weitzenböck curvature ter…