Three-dimensional steady gradient Ricci solitons with linear curvature decay

Yuxing Deng; Xiaohua Zhu

doi:10.1093/imrn/rnx155

Three-dimensional steady gradient Ricci solitons with linear curvature decay

Yuxing Deng, Xiaohua Zhu^*

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

In this note, we prove that a three-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature R(x) satisfies (Equation presented) for some constant C₀ > 0, where ρ(x) denotes the distance from a fixed point x₀. Our result does not assume that the soliton is κ-noncollapsed.

Original language	English
Pages (from-to)	1108-1124
Number of pages	17
Journal	International Mathematics Research Notices
Volume	2019
Issue number	4
DOIs	https://doi.org/10.1093/imrn/rnx155
Publication status	Published - 20 Feb 2019
Externally published	Yes

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title = "Three-dimensional steady gradient Ricci solitons with linear curvature decay",

abstract = "In this note, we prove that a three-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature R(x) satisfies (Equation presented) for some constant C0 > 0, where ρ(x) denotes the distance from a fixed point x0. Our result does not assume that the soliton is κ-noncollapsed.",

author = "Yuxing Deng and Xiaohua Zhu",

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AU - Deng, Yuxing

AU - Zhu, Xiaohua

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Y1 - 2019/2/20

N2 - In this note, we prove that a three-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature R(x) satisfies (Equation presented) for some constant C0 > 0, where ρ(x) denotes the distance from a fixed point x0. Our result does not assume that the soliton is κ-noncollapsed.

AB - In this note, we prove that a three-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature R(x) satisfies (Equation presented) for some constant C0 > 0, where ρ(x) denotes the distance from a fixed point x0. Our result does not assume that the soliton is κ-noncollapsed.

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DO - 10.1093/imrn/rnx155

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VL - 2019

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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Three-dimensional steady gradient Ricci solitons with linear curvature decay

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