The support of the limit distribution of optimal Riesz energy points on sets of revolution in ![[openface R]](http://scitation.aip.org/servlet/GetImg?key=JMAPAQ000048000012122901000001%3A0%3A0%3A28&t=a&d=a)
3
Let A be a compact point set in the right half of the xy plane and (A) the set in 3 obtained by rotating A about the y axis. We investigate the support of the limit distribution of minimal energy poin...
Let A be a compact point set in the right half of the xy plane and (A) the set in 3 obtained by rotating A about the y axis. We investigate the support of the limit distribution of minimal energy poin...
An exact fluid model for relativistic electron beams: The many moment case
An interesting and satisfactory fluid model has been proposed in literature for the description of relativistic electron beams. It was obtained with 14 independent variables by imposing the entropy pr...
An interesting and satisfactory fluid model has been proposed in literature for the description of relativistic electron beams. It was obtained with 14 independent variables by imposing the entropy pr...
On convex surfaces with minimal moment of inertia
J. Math. Phys. 48, 122902 (2007); doi:10.1063/1.2823888
Published 28 December 2007
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We investigate the problem of minimizing the moment of inertia among convex surfaces in ![[openface R]](http://scitation.aip.org/servlet/GetImg?key=JMAPAQ000048000012122902000001%3A0%3A0%3A28&t=a&d=a)
3 having a specified surface area. First, we prove that a minimizing surface exists, and derive a necessary condition holding at points of positive curvature. Then we show that an equilateral triangular prism is the optimal triangular prism, that the cube is the optimal rectangular prism, and that the sphere is (locally) optimal among ellipsoids. Many examples of convex surfaces are examined, among which the lowest moment of inertia is achieved by a truncated tetrahedron. The problem of finding the global minimizing surface remains open. The analogous problem in two dimensions has been solved by Sachs and later by Hall, who showed that the equilateral triangle minimizes the moment of inertia, among all convex curves with given length.
©2007 American Institute of Physics
| History: | Received 8 June 2007; accepted 17 November 2007; published 28 December 2007 |
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