A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons

Abstract

We prove that a shrinking gradient Ricci soliton which agrees to infinite order at spatial infinity with one of the standard cylindrical metrics on $S^k\times \RR^{n-k}$ for $k\ge 2$ along some end must be isometric to the cylinder on that end. When the underlying manifold is complete, it must be globally isometric either to the cylinder or (when $k=n-1$) to its $\ZZ_2$-quotient.

v2: Minor corrections; 66 pages, no figures

References in corpus (3)

• Ricci flow with surgery on three-manifolds
• Geometry of shrinking Ricci solitons
• Four-dimentional Gradient Shrinking Solitons with Positive Isotropic Curvature