Geodesic
On a conjecture by Auerbach
Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1633-1676 Cet article a éte moissonné depuis la source EMS Press

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In 1938 Herman Auerbach published a paper where he showed a deep connection between the solutions of the Ulam problem of floating bodies and a class of sets studied by Zindler, which are the planar sets whose bisecting chords all have the same length. In the same paper he conjectured that among Zindler sets the one with minimal area, as well as with maximal perimeter, is the so-called “Auerbach triangle”. We prove this conjecture.
DOI : 10.4171/jems/290
Classification : 49-XX, 00-XX
Keywords: Min-max problems, minimal area, Zindler sets, optimal convex sets 
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     author = {Nicola Fusco and Aldo Pratelli},
     title = {On a conjecture by {Auerbach}},
     journal = {Journal of the European Mathematical Society},
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     year = {2011},
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     number = {6},
     doi = {10.4171/jems/290},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/290/}
}
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Nicola Fusco; Aldo Pratelli. On a conjecture by Auerbach. Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1633-1676. doi: 10.4171/jems/290

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