https://neckpinch.com/authors/tsz-kiu-aaron-chow/New arXiv papers by Tsz-Kiu Aaron Chow, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.25610arxiv:2610.25610Mon, 19 Oct 2026 00:00:00 GMTTsz-Kiu Aaron Chow — We develop a pinching method for mean curvature flow in higher codimension. Motivated by pinching constructions for Ricci flow, the method uses a nonlinear deformation of the second fundamental form. We introduce two tensorial curvature conditions for closed immersions in Euclidean space which extend beyond the scope of classical scalar pinching results. In dimensions at least ten, we apply the method to prove convergence to a round point under the first condition and a canonical neighborhood theorem under the second.Ricci flowMean curvature flowCurvature pinching https://arxiv.org/abs/2608.18002arxiv:2608.18002Tue, 18 Aug 2026 00:00:00 GMTTsz-Kiu Aaron Chow, Jingbo Wan — For m=2,3, we prove that every smooth immersion F:ℝℙ^mlooparrowrightoverline{B^(,N)(1) satisfies κ(F)²≥ 2m/(m+1), with equality only for the Veronese embedding, up to congruence. We also prove that a closed, connected, orientable three-manifold admitting an immersion into a Euclidean unit ball with κ(F)≤√(3/2) is diffeomorphic to S³, ℝℙ³, or S²× S¹. All three possibilities occur, while κ(F)<√(3/2) forces X≅ S³. These results answer a question of Petrunin and prove a conjecture of Chodosh–Li concerning the normal curvature of three-manifolds. The key intrinsic input is the strict scalar–systolic inequality (min_Y R_g)sys(g)²<6π² for every spherical three-space form Y with |π₁(Y)|>2. Its proof uses systolic monotonicity along Ricci flow with surgery. This strict inequality complements the sharp scalar–systolic inequality for ℝℙ³ of Bray–Brendle–Eichmair–Neves.Ricci flowSurgery3-manifoldsSphere theorems https://arxiv.org/abs/2601.01863arxiv:2601.01863Mon, 05 Jan 2026 00:00:00 GMTTsz-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 energy for spinors. We compute its first variation formula, and show that its critical points under natural constraints are twisted Ricci solitons and eigen-spinsors of the weighted Dirac operator. We introduce a negative L^2-gradient flow of this functional, and establish its short-time existence and uniqueness via contraction mapping methods.Ricci solitonsPerelman entropyStability & uniquenessHarmonic maps & DeTurck trick