2024/03/25 by Zichang Liu, Liu, Zichang · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Bounded function #Center of curvature #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Geometry #Geophysics and Gravity Measurements #Mathematical analysis #Mathematics #Mean curvature #Mean curvature flow
paper · pdf · doi:10.48550/arxiv.2403.16515
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/03/25 · openalex created_date 2024/03/27 · openalex updated_date 2026/07/28
In 1994, Velázquez constructed a countable family of complete hypersurfaces flowing in ℝ2N (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.