A round ball uniquely minimizes gravitational potential energy

Frank Morgan
2005 Proceedings of the American Mathematical Society  
We give a proof following Carleman that among measurable bodies in R 3 of mass m 0 and density at most 1, a round ball of unit density uniquely minimizes gravitational potential energy.
doi:10.1090/s0002-9939-05-08070-6 fatcat:rn4cb4zklfaqtch2gppfwoivp4