https://neckpinch.com/authors/pak-tung-ho/New arXiv papers by Pak Tung Ho, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2606.27164arxiv:2606.27164Thu, 25 Jun 2026 00:00:00 GMTClaudio Afeltra, Andrea Pinamonti, Pak Tung Ho — We construct a contact form on a three dimensional CR manifold such that the CR Yamabe flow fails to converge. More precisely, on small Rossi deformations of the standard CR three-sphere, we exhibit an example whose corresponding CR Yamabe flow develops a one-bubble concentration regime. The construction is based on the negativity of the pseudohermitian mass on the Rossi spheres. This shows that mass positivity is not merely a technical assumption in the known convergence results for the CR Yamabe flow, but is genuinely connected to the large-time dynamics of the flow.Yamabe flow3-manifolds https://arxiv.org/abs/2601.22934arxiv:2601.22934Fri, 30 Jan 2026 00:00:00 GMTPak Tung Ho, Cheikh Birahim Ndiaye, Liming Sun, Heming Wang — In this paper, we study the prescribed T-curvature problem on the unit ball B⁴ of ℝ ⁴ via the T-curvature flow approach. By combining Ache-Chang's inequality with the Morse-theoretic approach of Malchiodi-Struwe, we establish existence results under strong Morse-type inequalities at infinity. As a byproduct of our argument, we also prove the exponential convergence of the T-curvature flow on B⁴, starting from a Q-flat and minimal metric conformal to the standard Euclidean metric, to an extremal metric of Ache-Chang's inequality whose explicit expression was derived by Ndiaye-Sun.Other curvature flows4-manifoldsLong-time existence & convergenceKähler–Einstein & K-stability https://arxiv.org/abs/2601.02853arxiv:2601.02853Tue, 06 Jan 2026 00:00:00 GMTPak Tung Ho — Using a modified curve shortening flow, we construct λ-Angenent curve, which was first constructed by the shooting method.Curve shortening https://arxiv.org/abs/2507.22183arxiv:2507.22183Tue, 29 Jul 2025 00:00:00 GMTJingeon An-Lacroix, Hardy Chan, Pak Tung Ho — Since the seminal paper of Graham and Zworski (Invent. Math. 2003), conformal geometric problems are studied in the fractional setting. We consider the convergence of fractional Yamabe flow, which is previously known under small initial energy assumption. Inspired by the deep work of Brendle (J. Diff. Geom. 2005), we obtain the full convergence result for arbitrary initial energy, whenever the (fractional) positive mass conjecture is valid.Yamabe flowPhysics https://arxiv.org/abs/2407.08757arxiv:2407.08757Thu, 04 Jul 2024 00:00:00 GMTPak Tung Ho, Sanghoon Lee — Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study the convergence rate of the Q-curvature flow in this paper. In particular, we provide an example of a slowly converging Q₆-curvature flow in dimension 6, in constrast to the dimension 2 case, where the Q-curvature flow always converges exponentially.Yamabe flowOther curvature flowsLong-time existence & convergence https://arxiv.org/abs/2212.04367arxiv:2212.04367Wed, 28 Sep 2022 00:00:00 GMTPak Tung Ho, Jinwoo Shin, Zetian Yan — The weighted Yamabe flow was the geometric flow introduced to study the weighted Yamabe problem on smooth metric measure spaces. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study in this paper the convergence rate of the weighted Yamabe flow.Yamabe flowLimit spaces & RCD