标题：Curvature estimates for 4-dimensional gradient Ricci solitons
报告人: 曹怀东（里海大学）
时间: 2021年 5月25日, 9:00-10:00
地点: 腾讯会议ID：124 650 170, 密码：112233
邀请人：张雅山
摘要：Gradient Ricci solitons are special Riemannian manifolds which often arise as singularity models in the Ricci flow. They are also natural extensions of Einstein manifolds. In three dimensions, gradient shrinking Ricci solitons have been classified. However, it remains a challenge to understand general gradient Ricci solitons in higher dimensions. It is well-known that the information about volume growth rate and asymptotic curvature behavior are crucial in the study of complete noncompact Riemannian manifolds. In 2015, Munteanu and Jiaping Wang proved an important curvature estimate for 4-dimensional gradient shrinking Ricci solitons with bounded scalar curvature. In this talk, we shall discuss some recent progress, including an extension of the Munteanu-Wang result in the 4D shrinking case (joint with Ernani Ribeiro Jr. and Detang Zhou), and some analog curvature estimates for 4-dimensional gradient steady solitons (joint with my former student Xin Cui).
报告人简介：
曹怀东教授是国际知名数学家，现为美国里海大学 (Lehigh University) 数学系 A. Everett Pitcher 讲席教授，是著名期刊 《微分几何杂志》(Journal of Differential Geometry) 的执行主编。 曹怀东教授主要从事的研究领域是微分几何与非线性偏微分方程，在 Ricci 流，Kahler 几何, 极小曲面，Ricci 孤立子，Fano 流形的形变等多个方面做出了一系列重要贡献, 曾获 Alfred P. Sloan 研究奖、John Simon Guggenheim 奖、 国家杰出青年科学基金B类（海外学者）等多项荣誉。
