1. Characterization of balls by generalized Riesz energy
- Author
-
Jun O'Hara
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,Convex geometry ,Euclidean space ,General Mathematics ,Multiple integral ,010102 general mathematics ,Metric Geometry (math.MG) ,Codimension ,Characterization (mathematics) ,01 natural sciences ,Integral geometry ,010101 applied mathematics ,Distribution (mathematics) ,Differential Geometry (math.DG) ,Mathematics - Metric Geometry ,53C65, 60D05, 58A99 ,FOS: Mathematics ,0101 mathematics ,Energy (signal processing) ,Mathematics - Abstract
We show that balls, circles and 2-spheres can be identified by generalized Riesz energy among compact submanifolds of the Euclidean space that are either closed or with codimension 0, where the Riesz energy is defined as the double integral of some power of the distance between pairs of points. As a consequence, we obtain the identification by the interpoint distance distribution., 9 pages, 2 figures
- Published
- 2018