NDLI: On the asymptotic behavior of expanding gradient Ricci solitons

Content Provider	Springer Nature Link
Author	Chen, Chih Wei
Copyright Year	2012
Abstract	Let (M, g, f) be an n-dimensional expanding gradient Ricci soliton with faster-than-quadratic-decay curvature, i.e., $${\lim_{{\rm dist}(O,x)\rightarrow\infty} \|{\rm Sect}(x)\|\cdot {\rm dist}(O,x)^2=0}$$ . When M is simply connected at infinity and n ≥ 3, we show that its tangent cone at infinity must be a manifold and is isometric to $${\mathbb{R}^n}$$ . Here, we also assume that M has only one end for the simplicity of the statement. A crucial step to gain the regularity of the tangent cone at infinity is to prove that the injectivity radius grows linearly. This can be achieved by combining the curvature assumption and a lower bound estimate of volume ratio of all geodesic balls, which is attained as Theorem 3. On the other hand, we also study the asymptotic volume ratio of non-steady gradient Ricci solitons under other weaker conditions.
Starting Page	267
Ending Page	277
Page Count	11
File Format	PDF
ISSN	0232704X
Journal	Annals of Global Analysis and Geometry
Volume Number	42
Issue Number	2
e-ISSN	15729060
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-02-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ricci flow Expanding soliton Curvature decay Statistics for Business/Economics/Mathematical Finance/Insurance Group Theory and Generalizations Theoretical, Mathematical and Computational Physics Geometry Analysis
Content Type	Text
Resource Type	Article
Subject	Analysis Geometry and Topology

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