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Solitons for the inverse mean curvature flow
We investigate self-similar solutions to the inverse mean curvature flow in
Euclidean space. In the case of one dimensional planar solitons, we explicitly
classify all homothetic solitons and translators. Generalizing Andrews' theorem
that circles are the only compact homothetic planar solitons, we apply the
Hsiung-Minkowski integral formula to prove the rigidity of the hypersphere in
the class of compact expanders of codimension one. We also establish that the
moduli space of compact expanding surfaces of codimension two is big. Finally,
we update the list of Huisken-Ilmanen's rotational expanders by constructing
new examples of complete expanders with rotational symmetry, including
topological hypercylinders, called infinite bottles, that interpolate between
two concentric round hypercylinders.Comment: typos correcte
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