北航学术报告

---分析、偏微分方程与动力系统讨论班(2026春季第16讲)

Planar doubling nodal solutions to the Yamabe equation with maximal rank

孙黎明（中国科学院数学与系统科学研究院）

时间：2026年08月12日（周三）下午15:40-16:20

地点：北航学院路老主楼 主410

摘要: We construct two families of nodal solutions to the Yamabe equation, each concentrating along two planar circles. One family is conformally equivalent to the one previously obtained by Medina–Musso. The second family is a twisted variant of the first; it is new and is derived from ansatzes that are not Kelvin invariant, in contrast to a standard assumption in earlier works. In addition, in dimension 3 these solutions attain maximal rank. By means of a continuous family of conformal transformations, we then analyze the interaction of the two circles, which display a crossing phenomenon reminiscent, in some sense, of leap-frogging behavior in vortex dynamics.

报告人简介: 孙黎明，中国科学院数学与系统科学研究院副研究员，2017年博士毕业于美国罗格斯大学。2008-2021年先后在约翰霍普金斯大学和英属哥伦比亚大学担任访问助理教授。研究方向是几何分析和非线性偏微分方程，研究成果发表于Duke Math Journal., Advances in Math， J. Funct. Anal.，J. Lond. Math. Soc等重要学术期刊。

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