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Volume growth for gradient shrinking solitons of Ricci-harmonic flow

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Abstract

In this paper, we derive an estimate on the potential functions of complete noncompact gradient shrinking solitons of Ricci-harmonic flow, and show that complete noncompact gradient shrinking Ricci-harmonic solitons have Euclidean volume growth at most.

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References

  1. Cao H D, Zhou D T. On complete gradient shrinking Ricci solitons. J Diff Geom, 2010, 85: 175–186

    MathSciNet  MATH  Google Scholar 

  2. Cao H D, Zhu X P. A complete proof of the Poincare and geometrization conjectures-application of the Hamilton-Perelman theory of the Ricci flow. Asian J Math, 2006, 10: 165–492

    MathSciNet  MATH  Google Scholar 

  3. Chen B L. Strong uniqueness of the Ricci flow. J Diff Geom, 2009, 82: 363–382

    MATH  Google Scholar 

  4. Eells J, Sampson J. Harmonic mappings of Riemannian manifolds. Amer J Math, 1964, 86: 109–169

    Article  MathSciNet  MATH  Google Scholar 

  5. Kleiner B, Lott J. Notes on Perelman’s papers. Geom Topol, 2008, 12: 2587–2855

    Article  MathSciNet  MATH  Google Scholar 

  6. List B. Evolution of an extended Ricci flow system. Comm Anal Geom, 2008, 16: 1007–1048

    MathSciNet  MATH  Google Scholar 

  7. Muller R. Ricci flow coupled with harmonic map flow. Ann Sci Ecole Norm Super, in press

  8. Perelman G. The entropy Formula for the Ricci Flow and its Geometric Applications. arXiv: 0211159v1

  9. Sheng W M, Wu C. Rotationally symmetric translating soliton of H k-flow. Sci China Math, 2010, 53: 1011–1016

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Fei Yang

  2. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Fei Yang

  3. College of Science, Huazhong Agricultural University, Wuhan, 430070, China

    JingFang Shen

Authors
  1. Fei Yang
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  2. JingFang Shen
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Correspondence to JingFang Shen.

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Yang, F., Shen, J. Volume growth for gradient shrinking solitons of Ricci-harmonic flow. Sci. China Math. 55, 1221–1228 (2012). https://doi.org/10.1007/s11425-012-4361-7

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  • DOI: https://doi.org/10.1007/s11425-012-4361-7

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