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Curvature Estimates for Four-Dimensional Gradient Steady Ricci Solitons

  • Huai-Dong CaoEmail author
  • Xin Cui
Article
  • 16 Downloads

Abstract

In this paper, we derive certain curvature estimates for 4-dimensional gradient steady Ricci solitons either with positive Ricci curvature or with scalar curvature decay \(\lim _{x\rightarrow \infty } R(x)=0\).

Keywords

Curvature estimate Steady Ricci solitons 

Mathematics Subject Classification

53C21 53C25 53C44 

Notes

Acknowledgements

We are grateful to Ovidiu Munteanu and Jiaping Wang for sending us their paper [25], and its early version in July 2014, which motivated us to consider curvature estimates for 4D steady solitons. The first author also would like to thank Ovidiu Munteanu for very helpful discussions; part of the work was carried out when the first author was visiting University of Macau, where he was partially supported by Science and Technology Development Fund (Macao S.A.R.) Grant FDCT/016/2013/A1 and the RDG010 Project of the University of Macau.

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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA

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