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

Thang Do, Arnulf Jentzen, Benno Kuckuck

We prove that for every open $U\subseteq {\mathbb{R}}^n$ the spherical projection of every gradient trajectory $\theta (t)$, $t\ge 0$, of a definable $C^1$-potential $F \colon U \to \m…