Axisymmetric stationary surfaces for the moment of inertia
Abstract
We investigate axisymmetric surfaces in Euclidean space that are stationary for the energy $E_\alpha=\int_\Sigma |p|^\alpha\, d\Sigma$ . Using a phase plane analysis, we classify these surfaces under the assumption that they intersect the rotation axis orthogonally. We also provide applications of the maximum principle, characterizing closed stationary surfaces and compact stationary surfaces with circular boundary in the case $\alpha=-2$ . Finally, we prove that helicoidal stationary surfaces must in fact be rotational surfaces.
Fields of Study & Subjects
Mathematics and Applications
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Publication details
- Journal / source
- Proceedings of the Royal Society of Edinburgh Section A Mathematics
- Pages
- 1–27
- Publication date
- 7 January 2026
- Language
- EN