微分几何讨论班（2025春第8讲）

题目： Bounding smooth Levi-flat hypersurfaces in a Stein manifold

报告人：方汉隆 教授（北京大学）

时间：2025年6月11日 3:30-4:30

地点：沙河主E806

摘要： We are concerned with the problem of constructing a smooth Levi-flat hypersurface locally or globally attached to a real codimension two submanifold in $C^{n+1}$, or more generally in a Stein manifold, with elliptic CR singularities, a research direction originated from a fundamental and classical paper of E. Bishop. We prove that a compact smooth (or, real analytic) real codimension two submanifold, that is contained in the boundary of a smoothly bounded strongly pseudoconvex domain, with a natural and necessary condition called CR non-minimal condition at CR points and with two elliptic CR singular points bounds a smooth-up-to-boundary (real analytic-up-to-boundary, respectively) Levi-flat hypersurface. This answers a well-known question left open from the work of Dolbeault-Tomassini-Zaitsev, or a generalized version of a problem already asked by Bishop in 1965. Our study here reveals an intricate interaction of several complex analysis with other fields such as symplectic geometry and foliation theory. This is based on joint work with X. Huang, W. Yin, and Z. Zhou.

报告人简介：方汉隆, 北京大学数学学院助理教授，博士生导师。2018年博士毕业于美国罗格斯大学新布朗斯维克分校，2018年-2021年在美国威斯康辛大学麦迪逊分校从事博士后研究。研究领域是复几何与多复变函数，在GAFA、Adv. Math.、IMRN等国际重要数学期刊发表多篇论文。

邀请人：谢振肖