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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The longest shortest fence and the stability of fl
oating trees - Kawohl\, B (Universitt zu Kln)
DTSTART;TZID=Europe/London:20140402T151500
DTEND;TZID=Europe/London:20140402T161500
UID:TALK51743AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51743
DESCRIPTION:Over 50 years ago Polya stated the following probl
em. Given a plane convex set K (a piece of land)\,
nd the shortest curve (or fence) that bisects thi
s set into two subsets of equal area. Is it true t
hat this curve is never longer than the diameter o
f the circular disc of same area as K? Under the a
dditional assumption that K is centrosymmetric (i.
e\, K = -K) he gave a simple proof that this is in
deed the case. Without this assumption the questio
n is much harder to answer positively. This is joi
nt work with L. Esposito\, V.Ferone\, C. Nitsch an
d C. Trombetti. By the way\, a result of N. Fusco
and A. Pratelli states\, that if the\nfences are r
estricted to be straight line segments\, the answe
r is negative. In that case the longest shortest f
ence is attained for the Auerbach triangle and not
for the disc.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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