Steady Ricci solitons with horizontally ϵ-pinched Ricci curvature

Yuxing Deng; Xiaohua Zhu

doi:10.1007/s11425-020-1685-3

Steady Ricci solitons with horizontally ϵ-pinched Ricci curvature

Yuxing Deng, Xiaohua Zhu^*

^*此作品的通讯作者

数学学院

Peking University

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

In this paper, we prove that any κ-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontally ϵ-pinched Ricci curvature must be rotationally symmetric. As an application, we show that any κ-noncollapsed gradient steady Ricci soliton (Mⁿ, g, f) with nonnegative curvature operator must be rotationally symmetric if it admits a unique equilibrium point and its scalar curvature R(x) lim_r(x)→∞R(x)f(x) = C₀ sup_x∈MR(x) with satisfies C0>n−22.

源语言	英语
页（从-至）	1411-1428
页数	18
期刊	Science China Mathematics
卷	64
期	7
DOI	https://doi.org/10.1007/s11425-020-1685-3
出版状态	已出版 - 7月 2021

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Deng, Y., & Zhu, X. (2021). Steady Ricci solitons with horizontally ϵ-pinched Ricci curvature. Science China Mathematics, 64(7), 1411-1428. https://doi.org/10.1007/s11425-020-1685-3

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abstract = "In this paper, we prove that any κ-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontally ϵ-pinched Ricci curvature must be rotationally symmetric. As an application, we show that any κ-noncollapsed gradient steady Ricci soliton (Mn, g, f) with nonnegative curvature operator must be rotationally symmetric if it admits a unique equilibrium point and its scalar curvature R(x) limr(x)→∞R(x)f(x) = C0 supx∈MR(x) with satisfies C0>n−22.",

keywords = "53C25, 53C55, 58J05, Ricci flow, Ricci soliton, κ-solutions, ϵ-pinched curvature",

author = "Yuxing Deng and Xiaohua Zhu",

note = "Publisher Copyright: {\textcopyright} 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

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doi = "10.1007/s11425-020-1685-3",

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AB - In this paper, we prove that any κ-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontally ϵ-pinched Ricci curvature must be rotationally symmetric. As an application, we show that any κ-noncollapsed gradient steady Ricci soliton (Mn, g, f) with nonnegative curvature operator must be rotationally symmetric if it admits a unique equilibrium point and its scalar curvature R(x) limr(x)→∞R(x)f(x) = C0 supx∈MR(x) with satisfies C0>n−22.

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KW - Ricci soliton

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JO - Science China Mathematics

JF - Science China Mathematics

IS - 7

ER -

Steady Ricci solitons with horizontally ϵ-pinched Ricci curvature

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