分野別セミナー

Inverse mean curvature flow has been studied not only as a geometric flow but also for applications to prove various geometric inequalities. Analyzing solitons of a geometric flow is a natural way to understand the flow, so we will deal with solitons for the inverse mean curvature flow in this talk. In this point of view, several examples of the solitons are introduced. Classifications of rotationally symmetric solitons are provided according to the asymptotic behavior. The incompleteness for these solitons are observed in examples and then, the incompleteness of any translating soliton and homothetic solitons with restrict homothetic ratio can be proved by applying maximum principle. The area growth of the solitons are obtained.