Title | Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds in the null case |

Publication Type | Journal Article |

Year of Publication | 2015 |

Authors | Ngô, QAnh, Xu, X |

Journal | Communications in Mathematical Physics |

Volume | 334 |

Pagination | 193–222 |

ISSN | 0010-3616 |

Abstract | This is the second in our series of papers concerning positive solutions of the Einstein-scalar field Lichnerowicz equations. Let $(M,g)$ be a smooth compact Riemannian manifold without boundary of dimension $n \geqslant 3$, $f$ and $a \geqslant 0$ are two smooth functions on $M$ with $\int_M f dv_g < 0$, $\sup_M f>0$, and $\int_M a dv_g>0$. In this article, we prove two results involving the following equation arising from the Hamiltonian constraint equation for the Einstein-scalar field equation in general relativity |

URL | http://dx.doi.org/10.1007/s00220-014-2133-7 |

DOI | 10.1007/s00220-014-2133-7 |