学术报告会：Cohomogeneity one minimal submanifolds

报告题目：Cohomogeneity one minimal submanifolds

报 告 人： Paolo Piccione  （Great Bay University 教授）

报告时间：2026年3月27日周五15: 30

报告地点：S3-313

Abstract：I will talk about minimal submanifolds S of closed Riemannian M that are invariant by the isometric action of a compact connected Lie group G. Cohomogeneity one means that the quotient space S/G has dimension one. By the symmetry reduction principle of Hsiang–Lawson, such submanifolds correspond to geodesics in the orbit space M/G, endowed with a conformal metric which is singular on the boundary, I will discuss a result of existence of free boundary geodesics in this singular space, and present a related compactness result in the case of smooth boundary. Finally, I will discuss a bifurcation theoretic application for minimal spheres in elongated ellipsoids. The talk is based on joint works with R. Bettiol, D. Corona and F. Giannoni.

个人简介：

Paolo Piccione，巴西圣保罗大学终身教授、巴西科学院院士、巴西数学会前会长（2017-2023）。Paolo院士现任国际数学联盟（IMU）执行委员会委员（2023-2025）、巴西科学技术部数学咨询委员会成员、圣保罗大学（USP）数学与统计研究所研究委员会主席/研究委员会成员、巴西联邦圣保罗州基金委员会（Fapesp）数学和统计学评估委员会成员、学术期刊Revista Matemática Universitária》的总主编和《Matemática Contemporânea》的副主编等社会工作。Paoloy院士主要从事分歧理论、莫尔斯理论、变分法和几何变分问题、几何学和哈密顿系统等方面的研究，在Arch. Ration. Mech. Anal.、 J. Differential Geom.、 J. Algebra、Topology、Pacific J. Math.、Indiana Univ. Math. J.、Math. Z.等著名数学期刊发表150余篇高水平学术论文。