Inscribed radius estimates for inverse curvature flow in sphere and hyperbolic space

In this paper, we study a fully nonlinear inverse curvature flow in sphere and hyperbolic space, and prove a non-collapsing property for this flow using maximum principle. Precisely, when ambient space is sphere, we show that upon some conditions on speed function, the radius of the largest touching interior ball is bounded below by a multiple of the reciprocal of the speed. Where ambient space is hyperbolic, we obtain an upper bound of the curvature of the largest touching interior ball for star-shaped inverse mean curvature flow.