Abstract
In this paper we study the problem of minimizing the area for the chord-convex sets of given size, that is, the sets for which each bisecting chord is a segment of length at least 2. This problem has been already studied and solved in the framework of convex sets, though nothing has been said in the non-convex case. We introduce here the relevant concepts and show some first properties.
Both the authors have been supported through the ERC St.G. AnOpt- SetCon.
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Acciaio, B., Pratelli, A. (2015). On the Minimization of Area Among Chord-Convex Sets. In: Pratelli, A., Leugering, G. (eds) New Trends in Shape Optimization. International Series of Numerical Mathematics, vol 166. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-17563-8_1
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DOI: https://doi.org/10.1007/978-3-319-17563-8_1
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Online ISBN: 978-3-319-17563-8
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