A Numerical Stability Analysis of Mean Curvature Flow of Noncompact Hypersurfaces with Type-II Curvature Blowup: II (Q6657555)

The goal of the paper is to determine whether or not the results observed in the numerical simulations in [\textit{D. Garfinkle} et al., Nonlinearity 34, No. 9, 6539--6560 (2021; Zbl 1473.53103)] remain true when the rotational symmetry is absent. The authors carried out numerical simulations of mean curvature flow (MCF) originating from initial data by imposing sinusoidal angular dependence. It was shown that the asymptotic behavior of these solutions is qualitatively unaffected by this angular dependence. Moreover, the angular dependence disappears as time approaches the first singular time, and the singular behaviors approach those observed in either the rotationally-symmetric Near Class or Far Class, independent of the initially angular dependence; as a result this singularity behavior is stable