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On the planar dual Minkowski problem

Chen, Shibing; Li, Qi-Rui

Description

In this paper, we resolve the planar dual Minkowski problem, proposed by Huang et al. (2016) [31] for all positive indices without any symmetry assumption. More precisely, given any , and function f on , bounded by two positive constants, we show that there exists a convex body Ω in the plane, containing the origin in its interior, whose dual curvature measure has density f. In particular, if f is smooth, then ∂Ω is also smooth.

CollectionsANU Research Publications
Date published: 2018
Type: Journal article
URI: http://hdl.handle.net/1885/157358
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2018.05.010

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