Asian Journal of Mathematics

Volume 19 (2015)

Number 5

Structure at infinity of expanding gradient Ricci soliton

Pages: 933 – 950

DOI: http://dx.doi.org/10.4310/AJM.2015.v19.n5.a6

Authors

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)

Abstract

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.

Keywords

Ricci flow, expanding gradient Ricci soliton, asymptotic cone

2010 Mathematics Subject Classification

53-xx, 58-xx

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Published 20 November 2015