The Lp Minkowski problem for polytopes for negative p

Abstract

Existence of solutions to the Lp Minkowski problem is proved for all p less than 0. For the cirtical case of p=-n, which is known as the centro-affine Minkowski problem, this paper contains the main result in [71] as a special case.

Accepted by Indiana Univ. Math. J. arXiv admin note: text overlap with arXiv:1406.7503, arXiv:1409.7907

References in corpus (1)

• The Logarithmic Minkowski Problem

Cited by in corpus (2)

• The $L_p$-Minkowski problem for $-n<p<1$
• The Orlicz version of the $L_p$ Minkowski problem on $S^{n-1}$ for $-n<p<0$