Shifted inverse curvature flows in hyperbolic space

We introduce the shifted inverse curvature flow in hyperbolic space. This is a family of hypersurfaces space expanding by $$F^{-p}$$ with positive power p for smooth, symmetric, strictly increasing and 1-homogeneous function F principal curvatures some concavity properties. study maximal existence asymptotical behavior horo-convex hypersurfaces. In particular, $$0<p\le 1$$ we show that limiting shape solution always round as time approached. contrast to (non-shifted) flow, Hung Wang (Calc Var Part Differ Equ 54(1):119–126, 2015) constructed counterexample not necessarily round.