## Abstract

The L_{p}-Minkowski problem introduced by Lutwak is solved for p ≥ n + 1 in the smooth category. The relevant Monge-Ampère equation (0.1) is solved for all p > 1. The same equation for p < 1 is also studied and solved for p ∈ (- n - 1, 1). When p = - n - 1 the equation is interpreted as a Minkowski problem in centroaffine geometry. A Kazdan-Warner-type obstruction for this problem is obtained.

Original language | English |
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Pages (from-to) | 33-83 |

Number of pages | 51 |

Journal | Advances in Mathematics |

Volume | 205 |

Issue number | 1 |

DOIs | |

Publication status | Published - 10 Sept 2006 |

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