Planar Central Configurations of Four Equal Masses: Classification and Morse Indices

Xiaoxiang Huangfu; Huatong Shen

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arXiv · 2611.06465

Planar Central Configurations of Four Equal Masses: Classification and Morse Indices

Xiaoxiang Huangfu·Huatong Shen

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Abstract

We study the planar central configurations of four equal positive masses under homogeneous interactions with force exponent $A>2$. For $2 3$, this completes the classification for all $A>2$ and gives an affirmative answer to Problem 11 of Albouy, Cabral, and Santos. We also establish the nondegeneracy modulo rotation of these configurations and determine their Morse indices, confirming Hampton's Conjecture 2. Our proofs are based on analytic arguments and exact algebraic calculations.

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Xiaoxiang Huangfu, Huatong Shen. 2026-11-04. Planar Central Configurations of Four Equal Masses: Classification and Morse Indices. https://arxiv.org/abs/2611.06465

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