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{Mixed volume preserving curvature flows in hyperbolic space}

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We consider mixed volume preserving curvature flows in hyperbolic space. The curvature function F is supposed to be monotone, symmetric, homogeneous of degree 1 and either convex or concave and inverse concave. For initial compact hypersurfaces, which are strictly concave by horospheres, we prove long time existence and exponential convergence of the flow to a geodesic sphere of the same mixed volume as the initial hypersurface.