Research demonstrates ancient solutions for mean curvature flows in isoparametric submanifolds, highlighting limiting behaviors.
Mean curvature flows of isoparametric submanifolds in Euclidean spaces and spheres have been studied by Liu and Terng in {X.CT} and {X.C}. In particular, it was proved that such flows always have ancient solutions. This is also true for mean curvature flows of isoparametric hypersurfaces in hyperbolic spaces by a result of Reis and Tenenblat in {S.H.T}. In this paper, we study mean curvature flows of isoparametric submanifolds in hyperbolic spaces with arbitrary codimension. In particular, we will show that they always have ancient solutions and study their limiting behaviors.
No takes yet. Share an insight, caveat, or question.
Liu et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: