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On Gradient Ricci Solitons

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Abstract

In the first part of the paper we derive integral curvature estimates for complete gradient shrinking Ricci solitons. Our results and the recent work in M. Fernandez-Lopez and E. Garcia-Rio, Rigidity of shrinking Ricci solitons in Math. Z. (2011) classify complete gradient shrinking Ricci solitons with harmonic Weyl tensor. In the second part of the paper we address the issue of existence of harmonic functions on gradient shrinking Kähler and gradient steady Ricci solitons. Consequences to the structure of shrinking and steady solitons at infinity are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Ovidiu Munteanu

  2. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Natasa Sesum

Authors
  1. Ovidiu Munteanu
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  2. Natasa Sesum
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Correspondence to Natasa Sesum.

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Communicated by Jiaping Wang.

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Munteanu, O., Sesum, N. On Gradient Ricci Solitons. J Geom Anal 23, 539–561 (2013). https://doi.org/10.1007/s12220-011-9252-6

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  • DOI: https://doi.org/10.1007/s12220-011-9252-6

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