Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons

Details Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons

2011-05-30

arxiv.org/abs/1105.6028v1

Mathematics

Differential Geometry

Main results were represented in the workshop Ricci Solitons Days in Pisa, 4 April, 2011

Scientific paper

We study the asymptotic volume ratio of non-steady gradient Ricci solitons. Moreover, a local estimate of the volume ratio is obtained for expanding solitons which satisfy $\lim_{dist(O,x)\rightarrow\infty} |Sect|\cdot dist(O,x)^2=0$. Therefore, for such a soliton, we can show that it must have $\mathbb{R}^n$ as one of its tangent cone at infinity. (Here we assume that the soliton is simply connected at infinity, has only one end and $n\geq 3$.)

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