https://neckpinch.com/authors/taehun-lee/New arXiv papers by Taehun Lee, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.34274arxiv:2610.34274Sun, 25 Oct 2026 00:00:00 GMTBeomseok Goh, Taehun Lee — We study ancient solutions to curve shortening flow on a class of warped product surfaces. For closed embedded ancient solutions whose curves are not null-homotopic, we prove that graphicality at every time is equivalent to a uniform length bound as t→-∞, and that these properties hold whenever the length is o(√(−t)). Under an additional positivity condition on the linearized height equation, every such solution with bounded length is a family of slices. We derive backward convergence to a limiting circle from the length bound and prove slice rigidity by an L² estimate for the height perturbation.Curve shorteningAncient solutionsStability & uniquenessRotational symmetry & warped products https://arxiv.org/abs/2405.01062arxiv:2405.01062Thu, 02 May 2024 00:00:00 GMTKyeongsu Choi, Jiuzhou Huang, Taehun Lee — We construct an I-family of ancient graphical mean curvature flows over a minimal hypersurface in ℝⁿ⁺¹ of finite total curvature with the Morse index I by establishing exponentially fast convergence in terms of |x|²−t. As a corollary, we show that these ancient flows have finite total curvature and finite mass drop. Moreover, one family of these flows is mean convex by a pointwise estimate.Mean curvature flowAncient solutionsLong-time existence & convergenceMinimal & CMC surfaces https://arxiv.org/abs/2310.02668arxiv:2310.02668Wed, 04 Oct 2023 00:00:00 GMTKi-Ahm Lee, Taehun Lee — We consider a flow by powers of Gauss curvature under the obstruction that the flow cannot penetrate a prescribed region, so called an obstacle. For all dimensions and positive powers, we prove the optimal curvature bounds of solutions and all time existence with its long time behavior. We also prove the C¹ regularity of free boundaries under a uniform thickness assumption.Other curvature flowsGauss curvature flowFree boundary & capillaryLong-time existence & convergence https://arxiv.org/abs/2304.11617arxiv:2304.11617Sun, 23 Apr 2023 00:00:00 GMTKyeongsu Choi, Minhyun Kim, Taehun Lee — We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure μ with a positive smooth density f, any solution to the Lₚ Minkowski problem in ℝⁿ⁺¹ with p ≤ −n+2 is a hypersurface of class C^(1,1). This is a sharp result because for each p∈ [−n+2,1) there exists a convex hypersurface of class C^(1,1/(n+p-1)) which is a solution to the Lₚ Minkowski problem for a positive smooth density f. In particular, the C^(1,1) regularity is optimal in the case p=−n+2 which includes the logarithmic Minkowski problem in ℝ³.Other curvature flowsGauss curvature flowAnisotropic & nonlocal flows