Rigidity of 4-dimensional Shrinking Ricci solitons
数学学科创建110周年系列报告
报告题目(Title)：Rigidity of 4-dimensional Shrinking Ricci solitons
报告人(Speaker)：周德堂 教授（巴西Fluminense联邦大学）
地点(Place)：后主楼1220
时间(Time)：2025年7月11日（星期五）16:00-17:00
邀请人(Inviter)：彦文娇
报告摘要
Perelman defined his W-functional and proved the entropy monotonicity formulae for Hamilton's Ricci flow. The critical points of W-functional are shrinking gradient Ricci solitons(SGRS). It is well known that gradient Ricci solitons are generalizations of Einstein manifolds and basic models for smooth metric measure spaces. In this talk I will discuss some recent progress and problems in four-dimensional cases. One of the challenging problems is to classify all gradient Ricci solitons with constant scalar curvature. Recently in a joint work with X. Cheng, we prove that a 4-dimensional shrinking gradient Ricci soliton has constant scalar curvature if and only if it is either Einstein, or a finite quotient of Gaussian shrinking soliton R^4, S^2×R^2 or S^3×R.
主讲人简介
周德堂，巴西 Fluminense联邦大学教授。 1991年博士毕业于山东大学。曾为山东大学教授，复旦大学、日本东北大学博士后，IMPA、 IHES、加州大学、 MIT等访问教授。研究成果发表在 J. Diff. Geom., Crelle，Amer. J. Math.，Trans. Amer. Math. Soc., Math. Ann.，
CVPDE等国际著名期刊上 。
