The Lp chord Minkowski problem

Abstract

Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn{{\mathbb{R}}}^{n}, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the Lp{L}_{p} chord measures is called the Lp{L}_{p} chord Minkowski problem in the Lp{L}_{p} Brunn-Minkowski theory, which includes the Lp{L}_{p} Minkowski problem as a special case. This article solves the Lp{L}_{p} chord Minkowski problem when p>1p\gt 1 and the symmetric case of 0<p<10\lt p\lt 1.

Keywords

• chord integral
• chord measure
• lp surface area measure
• lp chord measure
• lp minkowski problem
• lp chord minkowski problem
• 52a38