On a conjecture by Auerbach

  • Nicola Fusco

    Università degli Studi di Napoli Federico II, Italy
  • Aldo Pratelli

    Universität Erlangen-Nürnberg, Germany


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.

Cite this article

Nicola Fusco, Aldo Pratelli, On a conjecture by Auerbach. J. Eur. Math. Soc. 13 (2011), no. 6, pp. 1633–1676

DOI 10.4171/JEMS/290