https://neckpinch.com/authors/beomseok-goh/New arXiv papers by Beomseok Goh, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.34274/arxiv: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