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In this paper, we consider a translating soliton for the inverse meancurvature flow given as a graph of a function on a domain in a unit spherewhose level sets give isoparametric foliation. First, we show that suchfunction is given as a composition of an isoparametric function on the unitsphere and a function which is given as a solution of a certain ordinarydifferential equation. Further, we analyze the shape of the graphs of thesolutions of the ordinary differential equation. This analysis leads to theclassification of the shape of such translating solitons for the inverse meancurvature flow.

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