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- W2787434455 abstract "In this paper we study properties of the area evolute (AE) and the center symmetry set (CSS) of a convex planar curve $gamma$. The main tool is to define a Minkowski plane where $gamma$ becomes a constant width curve. In this Minkowski plane, the CSS is the evolute of $gamma$ and the AE is an involute of the CSS. We prove that the AE is contained in the region bounded by the CSS and has smaller signed area. The iteration of involutes generate a pair of sequences of constant width curves with respect to the Minkowski metric and its dual, respectively. We prove that these sequences are converging to symmetric curves with the same center, which can be regarded as a central point of the curve $gamma$." @default.
- W2787434455 created "2018-02-23" @default.
- W2787434455 creator A5070780598 @default.
- W2787434455 date "2013-01-27" @default.
- W2787434455 modified "2023-09-24" @default.
- W2787434455 title "Affine Evolutes and Symmetry of Convex Planar Curves" @default.
- W2787434455 hasPublicationYear "2013" @default.
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