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Article overview
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Equilibria and energy minimizers for an interaction model on the hyperbolic space | | Razvan C. Fetecau
; Hansol Park
; | | Date: |
1 Jun 2022 | | Abstract: | We study an intrinsic model for collective behaviour on the hyperbolic space
$bh^dm$. We investigate the equilibria of the aggregation equation (or
equivalently, the critical points of the associated interaction energy) for
interaction potentials that include Newtonian repulsion. By using the method of
moving planes, we establish the radial symmetry and the monotonicity of
equilibria supported on geodesic balls of $bh^dm$. We find several explicit
forms of equilibria and show that one such equilibrium is a global energy
minimizer. We also consider more general potentials and utilize a technique
used for $br^dm$ to establish the existence of compactly supported global
minimizers. Numerical simulations are presented, suggesting that some of the
equilibria studied here are global attractors. The key tool in our
investigations is a family of isometries of $bh^dm$ that we have developed
for this purpose. | | Source: | arXiv, 2206.00197 | | Services: | Forum | Review | PDF | Favorites | |
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