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News/On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials
arxiv
PublishedOctober 22, 2026 at 4:00 AM

On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials

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arXiv:2610.29211v1 Announce Type: cross Abstract: We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $\theta(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has finite length and, in particular, converges (directi

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