The longest shortest fence and sharp Poincaré-Sobolev inequalities

Details The longest shortest fence and sharp Poincaré-Sobolev inequalities The longest shortest fence and sharp Poincaré-Sobolev inequalities

2010-11-29

arxiv.org/abs/1011.6248v1

Mathematics

Optimization and Control

30 pages, 12 figures

Scientific paper

We prove a long standing conjecture concerning the fencing problem in the plane: among planar convex sets of given area, prove that the disc, and only the disc maximizes the length of the shortest area-bisecting curve. Although it may look intuitive, the result is by no means trivial since we also prove that among planar convex sets of given area the set which maximizes the length of the shortest bisecting chords is the so-called Auerbach triangle.

Affiliated with

Also associated with

No associations

Rating

The longest shortest fence and sharp Poincaré-Sobolev inequalities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The longest shortest fence and sharp Poincaré-Sobolev inequalities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The longest shortest fence and sharp Poincaré-Sobolev inequalities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-221149