A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons

Brett Kotschwar; Lu Wang

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arXiv · 1712.03185

A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons

Brett Kotschwar·Lu Wang

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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 $k\geq 2$ 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.

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Brett Kotschwar, Lu Wang. 2017-12-08. A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons. https://arxiv.org/abs/1712.03185

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