Geometry & Topology Seminar

Hamilton-Ivey estimates for gradient Ricci solitons

  • 演讲者:陈柏杨(加州大学圣地亚哥分校)

  • 时间:2022-07-12 10:00-11:00

  • 地点:Zoom ID 96277559519, Passcode 409679

Abstract 

One special feature for the Ricci flow in dimension 3 is the Hamilton-Ivey estimate. The curvature pinching estimate provides a lot of information about the ancient solution and plays a crucial role in the singularity formation of the flow in dimension 3. We study the pinching estimate on 3 dimensional expanding and 4 dimensional steady gradient Ricci solitons. A sufficient condition for a 3-dimensional expanding soliton to have positive curvature is established. This condition is satisfied by a large class of conical expanders. As an application, we show that any 3-dimensional gradient Ricci expander C^2 asymptotic to certain cones is rotationally symmetric. We also prove that the norm of the curvature tensor is bounded by the scalar curvature on 4 dimensional non Ricci flat steady soliton singularity model and derive a quantitative lower bound of the curvature operator for 4-dimensional steady solitons with linear scalar curvature decay and proper potential function. This talk is based on a joint work with Zilu Ma and Yongjia Zhang. 


报告人简介:陈柏扬,加州大学圣地亚哥分校博士后研究员。2020 年于明尼苏达大学取得博士学位。其研究领域为微分几何与几何分析,特别是 Ricci 孤立子的研究,其工作发表在 J. Funct. Anal., IMRN 等国际期刊上。