The $L_p$ Aleksandrov problem for origin-symmetric polytopes

Abstract

The $L_p$ Aleksandrov integral curvature and its corresponding characterization problem---the $L_p$ Aleksandrov problem---were recently introduced by Huang, Lutwak, Yang, and Zhang. The current work presents a solution to the $L_p$ Aleksandrov problem for origin-symmetric polytopes when $-1<p<0$.

References in corpus (7)

• The Logarithmic Minkowski Problem
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Relative entropy of cone measures and $L_p$ centroid bodies
• The dual Minkowski problem for negative indices
• On the uniqueness of $L_p$-Minkowski problems: the constant $p$-curvature case in ${\mathbb{R}}^3$
• The $L_p$ dual Minkowski problem for $p>1$ and $q>0$
• The dual Minkowski problem for symmetric convex bodies