On a conjecture by Auerbach

Fusco, Nicola, and Pratelli, A.. "On a conjecture by Auerbach." Journal of the European Mathematical Society 013.6 (2011): 1633-1676. <http://eudml.org/doc/277516>.

@article{Fusco2011,
abstract = {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.},
author = {Fusco, Nicola, Pratelli, A.},
journal = {Journal of the European Mathematical Society},
keywords = {min-max problems; minimal area; Zindler sets; optimal convex sets; min-max problems; minimal area; zindler sets; optimal convex sets},
language = {eng},
number = {6},
pages = {1633-1676},
publisher = {European Mathematical Society Publishing House},
title = {On a conjecture by Auerbach},
url = {http://eudml.org/doc/277516},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Fusco, Nicola
AU - Pratelli, A.
TI - On a conjecture by Auerbach
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 6
SP - 1633
EP - 1676
AB - 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.
LA - eng
KW - min-max problems; minimal area; Zindler sets; optimal convex sets; min-max problems; minimal area; zindler sets; optimal convex sets
UR - http://eudml.org/doc/277516
ER -