报告题目：Stability of Sobolev inequalities on manifolds with Ricci curvature lower bounds

报告摘要：The stability problem for the Sobolev inequality in Euclidean space asks whether functions that nearly achieve equality must be close to the family of optimizers. This question has attracted significant attention in recent years, and stability estimates are by now well understood. In contrast, on Riemannian manifolds, the presence of curvature gives rise to new phenomena and leads to novel stability questions even in the absence of optimizers. In this talk, we present recent results on the stability of Sobolev inequalities on Riemannian manifolds, obtained in collaboration with D. Parise and I. Y. Violo. After a brief overview of the Euclidean theory as motivation, we discuss both quantitative and qualitative stability results for different Sobolev-type inequalities of geometric and functional nature. Particular attention will be devoted to the role of Ricci curvature lower bounds and to the use of nonsmooth methods, including generalized concentration-compactness principles. Along the way, we discuss some problems and perspectives under nonnegative curvature assumptions.

报告人简介：Francesco Nobili，意大利那不勒斯费德里科二世大学数学系助理教授（tenure-track，RTT）。2015年获都灵理工大学数学工程学士学位，2017年获洛桑联邦理工学院应用数学硕士学位，2021年获意大利国际高等研究院（SISSA）数学博士学位，导师为 Nicola Gigli。曾在芬兰于韦斯屈莱大学及意大利比萨大学从事博士后研究，2026年6月起任现职。主要研究方向为几何分析、度量几何、几何与函数不等式、度量测度空间及 Sobolev 不等式的定量稳定性。代表性成果发表于 Adv. Math.、Int. Math. Res. Not.、JFA、CVPDE 及 Trans. Amer. Math. Soc. 等国际期刊，涉及黎曼流形上的 Sobolev 不等式稳定性、Pólya–Szegő 重排不等式、度量空间上的梯度流以及平面铺砌的几何问题。

报告时间：2026年10月28日 10:50-11:50  Talk

                 16:20-15:20 Faculty Research Discussion

                 17:30-21:30 Graduate Research Mentoring

报告地点：同析4号楼412会议室