https://neckpinch.com/authors/zichang-liu/New arXiv papers by Zichang Liu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2403.16515/arxiv:2403.16515Mon, 25 Mar 2024 00:00:00 GMTZichang Liu — In 1994, Velázquez constructed a countable family of complete hypersurfaces flowing in ℝ^(2N) (N≥ 4) by mean curvature, each of which develops a type II singularity at the origin in finite time. Later Guo and Sesum showed that for a non-empty subset of Velázquez's solutions, the mean curvature blows up near the origin, at a rate smaller than that of the second fundamental form; recently Stolarski proved another subset of these solutions has bounded mean curvature up to the singular time. In this paper, we follow their arguments to construct compact mean curvature flow solutions in ℝⁿ (n≥ 8) with bounded mean curvature.Mean curvature flowSingularities