On eternal mean curvature flows of tori in perturbations of the unit sphere (Q2685166)

Let \(\mathbb{T} =\mathbb{S}^1 \times \mathbb{S}^1\) be the standard 2-dimensional torus and \(\mathbb{S}^3\) be the standard unit sphere with constant curvature metric \(g\). The author show that there exists a generic subset \(\mathcal{U}\) of \(C^{\infty}(\mathbb{S}^3 )\) (i.e., the space of smooth functions over \(\mathbb{S}^3\) furnished with the topology of smooth convergence), for all \(u\in \mathcal{U}\), there exists \(\epsilon> 0\) such that, for all \(0 < |t| < \epsilon\), there exists a nontrivial eternal mean curvature flow \(e : \mathbb{T}\times \mathbb{R} \rightarrow (\mathbb{S}^3 , e^{ 2tu} g)\).