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We study solutions to the inverse mean curvature flow which evolve byhomotheties of a given submanifold with arbitrary dimension and codimension. Wefirst show that the closed ones are necessarily spherical minimal immersionsand so we reveal the strong rigidity of the Clifford torus in this setting.Mainly we focus on the Lagrangian case, obtaining numerous examples anduniqueness results for some products of circles and spheres that generalize theClifford torus to arbitrary dimension. We also characterize the pseudoumbilicalones in terms of soliton curves for the inverse curve shortening flow andminimal Legendrian immersions in odd-dimensional spheres. As a consequence, weclassify the rotationally invariant Lagrangian homothetic solitons for theinverse mean curvature flow.

Homothetic solitons for the inverse mean curvature flow