中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： 李阳垟 博士（University of Chicago）
题 目：Minimal hypersurfaces in a generic 8-dimensional closed Riemannian manifold
时 间：2023.06.19（星期一），09:00-10:00
地 点：MCM110 & Online
(Zoom ID: 3329836068 Password: mcm1234)
摘 要：In the past decade, the Almgren-Pitts min-max theory has advanced the theory of minimal hypersurfaces in a closed Riemannian manifold (M^{n+1}, g). Extensive research has been conducted on various properties of these minimal hypersurfaces, such as areas, Morse indices, multiplicities, and spatial distributions, when 3 ≤ n+1 ≤ 7. However, in higher dimensions, singularities may arise in the constructed minimal hypersurfaces. This occurrence invalidates many techniques that are effective in the low dimensions when investigating these geometric objects. In this talk, I will discuss how to overcome this difficulty in a generic 8-dimensional closed manifold, employing various deformation arguments. En route to obtaining generic results, we establish the generic regularity of minimal hypersurfaces in dimension 8. The talk is based on joint works with Zhihan Wang.
-----------------
华罗庚青年数学论坛学术报告
报告人： 李阳垟 博士（University of Chicago）
题 目：Existence and regularity of anisotropic minimal hypersurfaces
时 间：2023.06.20（星期二），09:00-10:00
地 点：MCM110 & Online
(Zoom ID: 3329836068 Password: mcm1234)
摘 要：Anisotropic area, a generalization of the area functional, arises naturally in models of crystal surfaces. Due to the absence of a monotonicity formula, the regularity theory for its critical points, anisotropic minimal surfaces, is significantly more challenging than the area functional case. In this talk, I will discuss how one can overcome this difficulty and obtain a smooth anisotropic minimal surface for elliptic integrands in closed 3-dimensional Riemannian manifolds via a min-max construction. This result confirms a conjecture by Allard [Invent. Math.,1983] in dimension 3. The talk is based on joint work with Guido De Philippis and Antonio De Rosa.
附件：