The discrete planar \(L_0\)-Minkowski problem
type: Item
instance of: scholarly article
title: The discrete planar \(L_0\)-Minkowski problem
zbMATH Open document ID: 1005.52002
author: Alina Stancu
published in: Advances in Mathematics
publication date: 2002-07-04T00:00:00Z
review text: The \(L_p\)-Minkowski problem, arising in Lutwak's Brunn-Minkowski-Firey theory of \(p\)-sums of convex bodies as an analogue to the classical Minkowski problem, is treated here for \(p= 0\) and planar polygons. This problem concerns the existence of a convex polygon in \(\mathbb{R}^2\), containing the origin, for which the direction of each edge and the area of the triangle formed by the edge and the origin are prescribed. If no two edges are parallel, the solution always exists. For the case where parallel edges occur, sufficient conditions for the existence are given. It is also shown that centrally symmetric data lead to centrally symmetry polygons. The proofs employ crystalline flows. For questions of uniqueness, a separate paper is announced.
reviewed by: Rolf Schneider
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 1763531
zbMATH Keywords: \(L_0\)-curvature
zbMATH Keywords: \(L_p\)-Minkowski problem
zbMATH Keywords: crystalline flows
MaRDI profile type: Publication
full work available at URL: aima.2001.2040
OpenAlex ID: W2089549495
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DOI: 10.1006/AIMA.2001.2040
description: scientific article; zbMATH DE number 1763531