Asian Journal of Mathematics

Volume 19 (2015)

Number 5

Structure at infinity of expanding gradient Ricci soliton

Pages: 933 – 950



Chih-Wei Chen (Department of Mathematics, National Taiwan University, Taipei, Taiwan)

Alix Deruelle (Département de mathématiques, Faculté des sciences, Université 11 Paris-Sud, Orsay, France)


We study the geometry at infinity of expanding gradient Ricci solitons $(M^n, g, \nabla f), n \geq 3$, with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a noncollapsed cone structure at infinity. Certain topological informations still can be obtained under conditions only involving asymptotic Ricci curvature ratio. Furthermore, we derive a quantitative relationship between (small) asymptotic curvature ratio and asymptotic volume ratio.


Ricci flow, expanding gradient Ricci soliton, asymptotic cone

2010 Mathematics Subject Classification

53-xx, 58-xx

Published 20 November 2015