Geometry of Complete Gradient Shrinking Ricci Solitons
arXiv:0903.3927
Abstract
We survey some of the recent progress on complete gradient shrinking Ricci solitons, including the classifications in dimension three and asymptotic behavior of potential functions as well as volume growths of geodesic balls in higher dimensions. This article is written for the conference proceedings dedicated to Yau's 60th birthday.
16 pages; updated version
References in corpus (5)
Cited by in corpus (16)
- On Bach-flat gradient shrinking Ricci solitons
- On the essential spectrum of complete non-compact manifolds
- Analysis of weighted Laplacian and applications to Ricci solitons
- Rigidity of asymptotically conical shrinking gradient Ricci solitons
- On complete gradient shrinking Ricci solitons
- On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking Ricci solitons
- On Potential Function of Gradient Steady Ricci Solitons
- On a classification of the quasi Yamabe gradient solitons
- Conical structure for shrinking Ricci solitons
- On gradient Ricci solitons
- A gap theorem of four-dimensional gradient shrinking solitons
- On rigidity of gradient Kähler-Ricci solitons with harmonic Bochner tensor
- Stability properties and gap theorem for complete -minimal hypersurfaces
- On the classification of noncompact steady quasi-Einstein manifold with vanishing condition on the Weyl tensor
- Sharp upper diameter bounds for compact shrinking Ricci solitons
- Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study