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

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Presentation transcript:

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

Ricci Flow and Basic

Cigar Soliton

Continued

Asymptotic Scalar Curvature Ratio

Continued

Behavior of Scalar Curvature

Continued: 3-dim’al

Maximum volume growth

Continued

Area of level sets

Continued

Volume of sublevel sets

Continued

Diameter growth