Higher dimensional steady Ricci solitons with linear curvature decay

Yuxing Deng; Xiaohua Zhu

doi:10.4171/JEMS/1003

Higher dimensional steady Ricci solitons with linear curvature decay

Yuxing Deng, Xiaohua Zhu

School of Mathematics and Statistics

Peking University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We prove that any noncompact κ-noncollapsed steady (gradient) Ricci soliton with nonnegative curvature operator must be rotationally symmetric if it has linear curvature decay.

Original language	English
Pages (from-to)	4097-4120
Number of pages	24
Journal	Journal of the European Mathematical Society
Volume	22
Issue number	12
DOIs	https://doi.org/10.4171/JEMS/1003
Publication status	Published - 5 Oct 2020

Keywords

Perelman's conjecture
Ricci flow
Ricci soliton
κ-solution

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title = "Higher dimensional steady Ricci solitons with linear curvature decay",

abstract = "We prove that any noncompact κ-noncollapsed steady (gradient) Ricci soliton with nonnegative curvature operator must be rotationally symmetric if it has linear curvature decay.",

keywords = "Perelman's conjecture, Ricci flow, Ricci soliton, κ-solution",

author = "Yuxing Deng and Xiaohua Zhu",

note = "Publisher Copyright: {\textcopyright} 2017 European Mathematical Society.",

year = "2020",

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doi = "10.4171/JEMS/1003",

language = "English",

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AB - We prove that any noncompact κ-noncollapsed steady (gradient) Ricci soliton with nonnegative curvature operator must be rotationally symmetric if it has linear curvature decay.

KW - Perelman's conjecture

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KW - κ-solution

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Higher dimensional steady Ricci solitons with linear curvature decay

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Keywords

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