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
偏微分方程研讨班
Speaker: 骆泳铭 副教授（深圳北理莫斯科大学）
Inviter: 范晨捷
Language: Chinese
Title: Sharp mass-threshold for Dancer-type solutions of the focusing mass-critical NLS on RdT1
Time & Venue: 2026年7月7日（星期二） 16:00-17:00 思源楼S813
Abstract: The mass-critical NLS on Euclidean space Rd exhibits a strong mass rigidity: all positive ground states are generated from a single profile and have the same ground state mass M_R(Q). By appealing to bifurcation methods, Dancer constructed solutions to the corresponding equation on RdT1 which decay in the noncompact directions and are nontrivially periodic in one direction. Such bifurcation approach, however, does not provide any energetic characterization of the solutions, and in particular does not explain their relation to the Euclidean ground-states. By introducing a new strict monotonicity mechanism for the prescribed-mass energy level, combining with the semivirial-vanishing geometry framework developed in a series of my recent works, we prove that for any mass less than |T|M_R(Q), the semivirial-vanishing variational problem admits a normalized Dancer-type optimizer which also solves the focusing mass-critical NLS on RdT1. This also gives a sharp complement for the existence results deduced in our earlier work via the Legendre-Fenchel duality.
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