Remarks on solitons for inverse mean curvature flow

Abstract

Homothetic and translating solitons for the inverse mean curvature flow (IMCF) in ℝ +1 are self-similar solutions deformed by only homothety and translation under IMCF, respectively. In this paper, we address some geometric properties of these solitons. To be specific, the incompleteness for the homothetic soliton of velocity with 0 < < 1 and for any translating soliton are proved. In addition, we show that the quantitative area growth for the homothetic solitons for ≥ 1 and the translating solitons. K E Y W O R D S homothetic soliton, inverse mean curvature flow, translating soliton M S C (2 0 1 0) 53A10, 53C44

Graphical translating solitons for the inverse mean curvature flow and isoparametric functions

“…For a translating soliton for the inverse mean curvature flow, Drugan, Lee, and Wheeler [5] gave a translating soliton in R 2 which is the cycloid generated by a circle with radius 1 4 and gave a tilted cycloid product as a translating soliton in R 3 . Kim and Pyo [8,9] showed the existence and classification of rotationally symmetric translating solitons in R n+1 and showed that there is no complete translating soliton for inverse mean curvature flow in R n+1 .…”