报告题目：Existence of stability optimizers for Yamabe-type inequalities

报告摘要：The well-known stability inequality due to Bianchi and Egnell (1991) bounds the deficit of the Sobolev inequality from below by a non-explicit positive constant times the -distance to the set of optimizers to the power two. While the power two is optimal, it is a major open question to determine the sharp value of . More recently, Engelstein, Neumayer and Spolaor (2022) have proved an analogous stability inequality for the Yamabe quotient on arbitrary closed Riemannian manifolds. The power two of the distance still appears generically, but explicit examples of manifolds are known for which degenerate stability occurs, i.e. the power of the distance is strictly higher than two. As a step towards determining the optimal stability constant , in this talk I will present an overview of recent results concerning the existence and non-existence of stability optimizers, both for Euclidean Sobolev inequalities and Yamabe inequalities on general manifolds, including the degenerate stability case. It turns out that the existence of stability optimizers displays a surprisingly rich behavior which depends in a remarkable way on the space dimension and other parameters.

报告人简介：Tobias König，德国法兰克福大学数学系几何变分方法方向 W1 tenure-track 教授. 现主持德国科学基金会（DFG）Emmy Noether 计划资助的“几何函数不等式及其稳定性”独立研究团队. 2020年获慕尼黑大学博士学位，师从 Rupert L. Frank，曾在巴黎及法兰克福从事博士后研究. 主要研究方向为变分法与偏微分方程，重点关注函数不等式及其稳定性、对称性与对称性破缺、椭圆方程的渐近分析，以及高阶与分数阶拉普拉斯算子相关问题. 在 J. Eur. Math. Soc.、Int. Math. Res. Not.、Comm. Partial Differential Equations、Anal. PDE、Adv. Math. 等国际期刊发表论文.

报告时间：2026年11月3日 19:30-21:30 Talk and Discussion

                2026年11月4日 19:30-21:30 Faculty Research Discussion

报告地点：同析4号楼412会议室