京师数学前沿论坛 第十九讲
京师数学前沿论坛
报告题目(Title)：Cohomogeneity one minimal submanifolds
报告人(Speaker)：Paolo Piccione 教授 （The University of São Paulo）
地点(Place)：后主楼1124
时间(Time)：2026年3月17日（周二）16:00-17:00
报告摘要
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.
主讲人简介
Paolo Piccione is a mathematician specializing in differential geometry, Riemannian geometry, and geometric analysis. He is a Full Professor in the Department of Mathematics at the University of São Paulo (USP), Brazil, and currently holds a Visiting Professorship at Great Bay University in Dongguan, China. His research focuses on submanifold theory, Morse theory, calculus of variations, partial differential equations, and bifurcation theory, with applications to general relativity and Hamiltonian systems. He served as President of the Brazilian Mathematical Society from 2017 to 2019 and has been a member of the Brazilian Academy of Sciences since 2012. He coordinates major research grants from FAPESP and CNPq on geometric analysis and variational problems, and has contributed to international mathematical governance through delegations to the International Mathematical Union.
