The Lp-Minkowski Problem and the Minkowski Problem in Centroaffine Geometry

Abstract

The Lp-Minkowski problem introduced by Lutwak is solved for p > n + 1 in the smooth category. The relevant Monge-Ampère equation (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… (More)

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Cite this paper

@inproceedings{Chou2005TheLP, title={The Lp-Minkowski Problem and the Minkowski Problem in Centroaffine Geometry}, author={Kai-Seng Chou and Xu-Jia Wang}, year={2005} }