Inverse Mean Curvature Flow and Infinite Bottles

We investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. Generalizing Andrews’ theorem that circles are the only compact homothetic planar solitons, we apply the Hsiung-Minkowski integral formula to prove the rigidity of hyperspheres in the class of compact expanders of codimension one. We update the list of Huisken-Ilmanen’s rotational expanders by con-structing new examples of complete expanders, including topological hypercylinders, called infinite bottles. This is joint work with Gregory Drugan and Glen Wheeler.