### Abstract

In this note we consider versions of both Ricci and sectional cur- vature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

Language | English (US) |
---|---|

Pages | 823-836 |

Number of pages | 14 |

Journal | Proceedings of the American Mathematical Society |

Volume | 144 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2016 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Some curvature pinching results for riemannian manifolds with density.** / Wylie, William.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 144, no. 2, pp. 823-836. https://doi.org/10.1090/proc/12853

}

TY - JOUR

T1 - Some curvature pinching results for riemannian manifolds with density

AU - Wylie, William

PY - 2016/2/1

Y1 - 2016/2/1

N2 - In this note we consider versions of both Ricci and sectional cur- vature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

AB - In this note we consider versions of both Ricci and sectional cur- vature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

UR - http://www.scopus.com/inward/record.url?scp=84951335472&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951335472&partnerID=8YFLogxK

U2 - 10.1090/proc/12853

DO - 10.1090/proc/12853

M3 - Article

VL - 144

SP - 823

EP - 836

JO - Proceedings of the American Mathematical Society

T2 - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -