1. Geometry of Gradient Ricci Solitons at Infinity Sun-Chin Chu Department of Mathematics Chung Cheng University

2. Outline 1. Equation and Basic 2. 2-dimensional Ricci Soliton: Cigar 3. Geometry at Infinity 4. Results on 3-dimensional Gradient Ricci Solitons Maximum volume Growth Behavior of Ricci curvature at Infinity Area Growth of level sets Volume Growth of sublevel Sets Diameter Growth

3. Ricci Flow and Basic

4. Cigar Soliton

5. Continued

6. Asymptotic Scalar Curvature Ratio

7. Continued

8. Behavior of Scalar Curvature

9. Continued: 3-dim’al

10. Maximum volume growth

11. Continued

13. Area of level sets

14. Continued

17. Volume of sublevel sets

18. Continued

19. Diameter growth