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- W2079495504 abstract "Our main result shows the uniqueness of planar convex polygons of given outer orientations to the sides and prescribed areas of the triangles formed by the origin with any two consecutive vertices, if they exist. Such polygons are solutions to the discrete L 0 -Minkowski problem in the plane proposed, in a larger generality, by Lutwak in his extension of the Brunn–Minkowski theory. The method exploits the equivalence between the L 0 -polygons and the homothetic solutions to appropriate anisotropic crystalline flows. Hence as a by-product we obtain a positive answer to Jean Taylor's conjecture on the uniqueness of polygonal shapes which are deformed homothetically under the flow by crystalline curvature, without any symmetry assumptions." @default.
- W2079495504 created "2016-06-24" @default.
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- W2079495504 date "2003-12-01" @default.
- W2079495504 modified "2023-10-03" @default.
- W2079495504 title "On the number of solutions to the discrete two-dimensional L0-Minkowski problem" @default.
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- W2079495504 doi "https://doi.org/10.1016/s0001-8708(03)00005-7" @default.
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