### Abstract

Let R be a constant. Let Mγ^{R} be the space of smooth metrics g on a given compact manifold Ω^{n} (n ≥ 3) with smooth boundary S such that g has constant scalar curvature R and g|ε is a fixed metric γ on S. Let V (g) be the volume of g ε Mγ^{R} . In this work, we classify all Einstein or conformally flat metrics which are critical points of V (.) in Mγ^{R}.

Original language | English (US) |
---|---|

Pages (from-to) | 2907-2937 |

Number of pages | 31 |

Journal | Transactions of the American Mathematical Society |

Volume | 363 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*363*(6), 2907-2937. https://doi.org/10.1090/S0002-9947-2011-05195-0

**Einstein and conformally flat critical metrics of the volume functional.** / Miao, Pengzi; Tam, Luen F.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 363, no. 6, pp. 2907-2937. https://doi.org/10.1090/S0002-9947-2011-05195-0

}

TY - JOUR

T1 - Einstein and conformally flat critical metrics of the volume functional

AU - Miao, Pengzi

AU - Tam, Luen F.

PY - 2011/6

Y1 - 2011/6

N2 - Let R be a constant. Let MγR be the space of smooth metrics g on a given compact manifold Ωn (n ≥ 3) with smooth boundary S such that g has constant scalar curvature R and g|ε is a fixed metric γ on S. Let V (g) be the volume of g ε MγR . In this work, we classify all Einstein or conformally flat metrics which are critical points of V (.) in MγR.

AB - Let R be a constant. Let MγR be the space of smooth metrics g on a given compact manifold Ωn (n ≥ 3) with smooth boundary S such that g has constant scalar curvature R and g|ε is a fixed metric γ on S. Let V (g) be the volume of g ε MγR . In this work, we classify all Einstein or conformally flat metrics which are critical points of V (.) in MγR.

UR - http://www.scopus.com/inward/record.url?scp=79952169663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952169663&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2011-05195-0

DO - 10.1090/S0002-9947-2011-05195-0

M3 - Article

VL - 363

SP - 2907

EP - 2937

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -