https://neckpinch.com/authors/qi-sun/New arXiv papers by Qi Sun, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.10197arxiv:2609.10197Wed, 09 Sep 2026 00:00:00 GMTAprameya Girish Hebbar, Guanhua Shao, Qi Sun — We show that on any closed orientable real-analytic Riemannian surface, any smoothly immersed closed immortal curve-shortening flow converges to a unique non-constant closed geodesic.Curve shorteningLong-time existence & convergence https://arxiv.org/abs/2510.14863arxiv:2510.14863Thu, 16 Oct 2025 00:00:00 GMTQi Sun — We show that any smooth closed immersed curve in ℝⁿ with a one-to-one convex projection onto some 2-plane develops a Type I singularity and becomes asymptotically circular under Curve Shortening flow in ℝⁿ. As an application, we prove an analog of Huisken's conjecture for Curve Shortening flow in ℝⁿ, showing that any smooth closed immersed curve in ℝⁿ can be smoothly perturbed to a closed immersed curve in ℝⁿ⁺² which shrinks to a round point under Curve Shortening flow. Our proof relies on a novel contradiction argument in which Type II singularities are excluded by proving both the uniqueness and non-uniqueness of the tangent flows at the singular point.Curve shorteningSingularitiesStability & uniqueness https://arxiv.org/abs/2509.16823arxiv:2509.16823Sat, 20 Sep 2025 00:00:00 GMTQi Sun — We establish a variant of Huisken's distance comparison principle for reflection symmetric immersed Curve Shortening flow in ℝⁿ,n≥2. As an application, we show that certain symmetric Curve Shortening flow with a one-to-one convex projection develops a Type I singularity and becomes asymptotically circular.Curve shorteningSingularities https://arxiv.org/abs/2410.08399arxiv:2410.08399Thu, 10 Oct 2024 00:00:00 GMTQi Sun — We show that under Space Curve Shortening flow any closed immersed curve in ℝⁿ whose projection onto ℝ²×\0\ is convex remains smooth until it shrinks to a point. Throughout its evolution, the projection of the curve onto ℝ²×\0\ remains convex. As an application, we show that any closed immersed curve in ℝⁿ can be perturbed to an immersed curve in ℝⁿ⁺² whose evolution by Space Curve Shortening shrinks to a point.Curve shortening