中国科学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
非线性泛函分析研讨班
Speaker: 朱超娜 教授 (宁波大学)
Inviter: 孙黎明
Language: Chinese
Title：Existence of prescribing scalar curvature problem on the negative Yamabe case
Time&Venue：2026年4月24日（星期五）10:00-11:00 & 思源楼 S817
Abstract: The problem of prescribing conformally the scalar curvature on a closed manifold of negative Yamabe invariant is always solvable if the function to be prescribed is strictly negative, while sufficient and necessary conditions are known in the case that function is non-positive. Still in the case of a negative Yamabe invariant, Rauzy showed solvability, if the function to be prescribed is not too positive. In this talk we will review these results variationally, show the existence of minimizability under smallness assumptions on K+ =
max{K, 0} and talk what happens when the relevant arguments fail to apply. At last, we will construct a function, for which saddle point solutions to the conformally prescribed scalar curvature problem still exist. In collaboration with Martin Mayer.
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Speaker: 赖善发 博士后 (澳门大学)
Inviter: 孙黎明
Language: Chinese
Title：Existence and Orbital Stability of Fully Localized Solitary Waves in 3D Capillary-Gravity Water Waves
Time&Venue：2026年4月24日（星期五）14:00-15:00 & 思源楼 S817
Abstract: This talk presents the existence and orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem. The existence is achieved via anisotropic scaling to the KP-I equation and refined estimates for the Dirichlet–to Neumann operator. Although the waves are constructed through a non-variational Lyapunov–Schmidt reduction, we prove their orbital stability up to spatial translations by adapting the Grillakis–Shatah–Strauss method.
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