The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry

Chou, Kai-Seng; Wang, Xu-Jia

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The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry

Date

2006

Authors

Chou, Kai-Seng

Wang, Xu-Jia

Publisher

Academic Press

Abstract

The Lp-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