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Solitons for the inverse mean curvature flow

Journal Article


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Abstract


  • 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 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 large. 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.

Authors


  •   Drugan, Gregory (external author)
  •   Lee, Hojoo (external author)
  •   Wheeler, Glen E.

Publication Date


  • 2016

Citation


  • Drugan, G., Lee, H. & Wheeler, G. (2016). Solitons for the inverse mean curvature flow. Pacific Journal of Mathematics, 284 (2), 309-326.

Scopus Eid


  • 2-s2.0-84991250056

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7222&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6192

Number Of Pages


  • 17

Start Page


  • 309

End Page


  • 326

Volume


  • 284

Issue


  • 2

Place Of Publication


  • United States

Abstract


  • 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 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 large. 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.

Authors


  •   Drugan, Gregory (external author)
  •   Lee, Hojoo (external author)
  •   Wheeler, Glen E.

Publication Date


  • 2016

Citation


  • Drugan, G., Lee, H. & Wheeler, G. (2016). Solitons for the inverse mean curvature flow. Pacific Journal of Mathematics, 284 (2), 309-326.

Scopus Eid


  • 2-s2.0-84991250056

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7222&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6192

Number Of Pages


  • 17

Start Page


  • 309

End Page


  • 326

Volume


  • 284

Issue


  • 2

Place Of Publication


  • United States