中科院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

偏微分方程研讨班

Speaker: 韩青 教授（University of Notre Dame）

Inviter: 邱国寰

Language: English

Title：A Parametrization of Solutions to the Yamabe Equation with Isolated Singularities

Time&Venue：2025年10月10日(星期五) 10:00-11:00&思源楼S615

Abstract: In this talk, we discuss solutions to the Yamabe equation with nonremovable isolated singularities. We parametrize these solutions by harmonic functions, or more precisely, by sequences of spherical harmonics. There is a one-to-one correspondence between the collection of the solutions to the Yamabe equation with nonremovable isolated singularities and the collection of the sequences of spherical harmonics through formal infinite series determined by the sequences of spherical harmonics. We prove that these formal infinite series yield actual solutions to the Yamabe equation with a nonremovable isolated singularity. These solutions to the Yamabe equation have designated asymptotic behaviors determined by the sequences of spherical harmonics. In a broader context, we provide a general method of constructing all solutions near its isolated singular points and all solutions near infinity.