Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons

Abstract

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 ${\lim }_{dist(O,x)\to \infty }|Sect|\cdot dist(O,x{)}^2=0$. 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 $n\ge 3$.)

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

References in corpus (5)

• The volume growth of complete gradient shrinking Ricci solitons
• Remarks on non-compact gradient Ricci solitons
• A lower bound for the scalar curvature of noncompact nonflat Ricci shrinkers
• Steady gradient soliton with curvature in L^1
• A necessary and sufficient condition for Ricci shrinkers to have positive AVR