Proper Riesz Equilibrium Support on Connected Sets of Revolution
Manuscript 21 October 2026 · Online 23 October 2026
Abstract
For every 0<s<1, we construct a connected compact set of revolution whose Riesz s-equilibrium measure omits a positive-capacity circle of its outer boundary. The generating set can also be chosen connected with nonempty interior. This gives an affirmative answer to the existential support question posed by Brauchart, Hardin and Saff. The construction combines their large-radius negative-distance kernel with a uniform polygonal domination inequality on the unit disk. A strict potential gap gives exact support exclusion at finite radius. The proof does not determine the equilibrium measure and does not require a numerical minimization. This is an unrefereed preprint, with source comparison, self-audit and exact arithmetic diagnostics; no independent or formal verification or absolute priority certification is asserted.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete proof in the stated sets-of-revolution scope
- Categories
- math.CA · math.MG
- Manuscript
- 21 October 2026
- Online release
- 23 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Proper Riesz Equilibrium Support on Connected Sets of Revolution,” EulerSolve Research Papers, OWR-1535-001, 2026. https://doi.org/10.5281/zenodo.23586519.
BibTeX
@misc{ferudun2026owr1535001,
author = {Ferudun, Alper},
title = {Proper Riesz Equilibrium Support on Connected Sets of Revolution},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-1535-001/},
doi = {10.5281/zenodo.23586519},
note = {OWR-1535-001; unrefereed preprint}
}