报告名称：Finiteness of Connected Components of the Singular Set in Mean Curvature Flow with Cylindrical Singularities

报告专家：曾令忠副教授

专家所在单位：江西师范大学

报告时间：2026年4月18日 14:30-18:30

报告地点:  数统学院201室

专家简介：

曾令忠，博士毕业于日本佐贺大学，现为江西师范大学数学与统计学院副教授，研究生导师。长期从事微分几何中特征值问题的研究，在Annales de l'Institut Henri Poincaré, Commun. Contemp. Math., Pacific J. Math., Science China Mathematics, J. Geom. Phys.等国内外重要学术期刊上发表论文20余篇，2020年获得江西省自然科学三等奖。

报告摘要：

In this talk, I will review some important results on singular sets of MCF and present a resolution of a conjecture by Colding and Minicozzi (2016) concerning the topological structure of the spacetime singular set in mean curvature flow (MCF). Specifically, I will show that for a MCF starting from a closed smooth embedded hypersurface and developing only cylindrical singularities, the singular set  S  consists of at most finitely many connected components.

If time permits, I will discuss applications of this result, including the regularity of the arrival time in the level set method and the stability of the component count under  C^2  perturbations of the initial data in the 2-convex case. This work completes the topological characterization of the singular set for generic MCF and extends tools that can be applicable to other geometric parabolic flows such as Ricci flow in our future work.