报告题目：Conformally invariant geometric inequalities

报 告 人：陈学长 教授（南京大学）

报告时间：2026年10月19日（星期一）15:30—16:30

报告地点：党建活动室111A

报告摘要：This is a survey on our works in conformally invariant geometric inequalities. We start with Lebedev-Millin inequality and its generalization, and the classical Szego limit theorem.  Inspired by the work of F. Hang and Alice Chang on the improved Moser-Trudinger-Onofri inequality, Shihong Zhang and I introduced an intermediate case between the first and second order moment constraints. Also we present our results (joint with Wei Wei and Nan Wu) of almost sharp Sobolev trace inequalities of orders two and four on the unit ball. Finally, we go back to the original motivation and present some perspectives in this direction.

报告人简介：南京大学数学学院教授、博士生导师，国家级青年人才。他的研究方向是几何分析与偏微分方程，研究兴趣主要集中于共形几何中的预定曲率问题（例如，带边Yamabe问题、带边σ2-曲率方程、预定Q-曲率问题等）及相关曲率流、带边流形上的几何不等式以及几何刚性现象等，相关论文发表在Invent. Math., Proc. Lond. Math. Soc., Adv. Math.等。