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SUMMARY:The longest shortest fence and the stability of floating trees - K
 awohl\, B (Universitt zu Kln)
DTSTART:20140402T141500Z
DTEND:20140402T151500Z
UID:TALK51743@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Over 50 years ago Polya stated the following problem. Given a 
 plane convex set K (a piece of land)\, nd the shortest curve (or fence) th
 at bisects this set into two subsets of equal area. Is it true that this c
 urve is never longer than the diameter of the circular disc of same area a
 s K? Under the additional assumption that K is centrosymmetric (i.e\, K = 
 -K) he gave a simple proof that this is indeed the case. Without this assu
 mption the question is much harder to answer positively. This is joint wor
 k with L. Esposito\, V.Ferone\, C. Nitsch and C. Trombetti. By the way\, a
  result of N. Fusco and A. Pratelli states\, that if the\nfences are restr
 icted to be straight line segments\, the answer is negative. In that case 
 the longest shortest fence is attained for the Auerbach triangle and not f
 or the disc.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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