Mathematics – Metric Geometry
Scientific paper
2008-12-13
Proceedings of the American Mathematical Society 138 (2010), 2863-2872
Mathematics
Metric Geometry
10 pages, to appear in Proceedings of the AMS
Scientific paper
10.1090/S0002-9939-10-10284-6
A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in R^3, and his classification is equivalent to the converse for R^3. In this paper we disprove the converse in high dimensions. We construct several counterexamples, including one with trivial symmetry group.
Cohn Henry
Elkies Noam D.
Kumar Abhinav
Schuermann Achill
No associations
LandOfFree
Point configurations that are asymmetric yet balanced 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 Point configurations that are asymmetric yet balanced, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Point configurations that are asymmetric yet balanced will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-249876