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, Volume 158, Issue 1–2, pp 223–234 | Cite as

Level set flow in 3D steady gradient Ricci solitons

  • Chih-Wei Chen
  • Kuo-Wei Lee


Given a nontrivial 3-dimensional steady gradient Ricci soliton, if the scalar curvature has decay order between \(-b\) and \(-a\) for some \(a\in (0,1], b\ge a\), then the umbilical ratio of the level set of the potential function lies in the class \(O(r^{6a-\frac{8a^2}{b}})\cap O(r^{2b-4a})\).

Mathematics Subject Classification

Primary 53C44 Secondary 53C25 


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The first author would like to thank Prof. Pengfei Guan for helpful discussions during the workshop for Besson’s 60th birthday. The second author is supported by the MOST research Grant 106-2115-M-018-002-MY2.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNational Kaohsiung Normal UniversityKaohsiungTaiwan
  2. 2.Department of MathematicsNational Changhua University of EducationChanghuaTaiwan

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