Arnold--Thom gradient conjecture

Let $\gamma(t)$ be a gradient flow line for an analytic function, and suppose that it has a limit point. Arnold--Thom gradient conjecture. The limit

$$\lim_{t\to\infty}\frac{\gamma'(t)}{\left|\gamma'(t)\right|}$$

exists. This is a stronger, first-order asymptotic statement than Thom's conjecture about convergence of secants. It remains open in general, although the paper proves it for arrival-time functions arising from mean curvature flows with neck or non-degenerate cylindrical singularities, including mean-convex flows of surfaces.