Lp Minkowski problem with not necessarily positive data

doi:10.1016/j.aim.2004.11.007

Advances in Mathematics

Volume 201, Issue 1, 20 March 2006, Pages 77-89

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Abstract

The $L_{p}$ Minkowski problem in the plane has been the object of a number of recent investigations. Here we present various existence results for $0 ⩾ p ⩾ - 2$ . In the case $0 > p > - 2$ , a necessary and sufficient condition for the solvability of the problem is given.

Keywords

L_{p}

Minkowski problem

Blaschke–Santalo inequality

Nonlinear equations

Variational methods

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¹: Partially supported by NSF Grant DMS-0072328.