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arXiv · 2609.00336

Critical points of point charge potentials along lines

Goncalo Oliveira
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Abstract

We prove Conjecture 1.9 of Gabrielov-Novikov-Shapiro. More precisely, for every $p>0$, every nonconstant restriction to a line of a potential generated by $n$ point charges has at most $2n-1$ critical points. The bound is sharp, even for positive charges. The proof uses a duality with an auxiliary planar potential generated by collinear charges and Morse theory.

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Goncalo Oliveira. 2026-08-31. Critical points of point charge potentials along lines. https://arxiv.org/abs/2609.00336

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