In this paper, we study self-expanding solutions to a large class ofparabolic inverse curvature flows by homogeneous symmetric functions ofprincipal curvatures in Euclidean spaces. These flows include the inverse meancurvature flow and many nonlinear flows in the literature. We first show that the only compact self-expanders to any of these flows areround spheres. Secondly, we show that complete non-compact self-expanders toany of these flows with asymptotically cylindrical ends must be rotationallysymmetric. Thirdly, we show that when such a flow is uniformly parabolic, thereexist complete rotationally symmetric self-expanders which are asymptotic totwo round cylinders with different radii. These extend some earlier results ofinverse mean curvature flow to a wider class of flows.
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