Geometry of Gradient Ricci Solitons at Infinity

Sun-Chin Chu

Department of Mathematics

Chung Cheng University

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

2

Ricci Flow and Basic

2Cigar Soliton

Continued

Asymptotic Scalar Curvature Ratio

Continued

Behavior of Scalar Curvature

Continued: 3-dim’al

Maximum volume growth

Continued

Continued

Area of level sets

Continued

Continued

Continued

Volume of sublevel sets

Continued

Diameter growth