Speaker: 方汉隆，北京大学

Inviter: 谢松晏副研究员

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

Language: Chinese

Time & Venue: 2024.11.12 10:00-11:30 思源楼525

Abstract: 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.