Lower Bound for the Green Energy of Point Configurations in Harmonic Manifolds

Lower Bound for the Green Energy of Point Configurations in Harmonic Manifolds

In this paper, we get the sharpest known to date lower bounds for the minimal Green energy of the compact harmonic manifolds of any dimension. Our proof generalizes previous ad-hoc arguments for the most basic harmonic manifold, i.e. the sphere, extending it to the general case and remarkably simpli...

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Veröffentlicht in:Potential analysis 2024-08, Vol.61 (2), p.247-261
Hauptverfasser: Beltrán, Carlos, de la Torre, Víctor, Lizarte, Fátima
Format: Artikel
Sprache:eng
Schlagworte:
Clean energy
Functional Analysis
Geometry
Lower bounds
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
Renewable energy
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Zusammenfassung:In this paper, we get the sharpest known to date lower bounds for the minimal Green energy of the compact harmonic manifolds of any dimension. Our proof generalizes previous ad-hoc arguments for the most basic harmonic manifold, i.e. the sphere, extending it to the general case and remarkably simplifying both the conceptual approach and the computations.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-023-10108-2