The planar $L_p$-Minkowski problem for $0< p<1$

TL;DR

This paper establishes necessary and sufficient conditions for solutions to the asymmetric $L_p$ Minkowski problem in two dimensions when $0 < p < 1$, advancing understanding of this geometric problem.

Contribution

It provides the first complete characterization of existence conditions for the asymmetric $L_p$ Minkowski problem in $ eal^2$ for the range $0 < p < 1$.

Findings

Necessary and sufficient conditions are identified.

The results apply specifically to the two-dimensional case.

The work advances the theory of the $L_p$ Minkowski problem.

Abstract

Necessary and sufficient conditions for the existence of solutions to the asymmetric $L_p$ Minkowski problem in $\mathbb{R}^2$ are established for $0 < p < 1$.