Title: Modified mean curvature flow of entire locally Lipschitz radial graphs in hyperbolic space,
Abstract: In a previous joint work of Xiao and the second author, the modified mean
curvature flow (MMCF) in hyperbolic space $\mathbb{H}^{n+1}$: $$\frac{\partial
\mathbf{F}}{\partial t} = (H-\sigma)\,\vnu\,,\quad \quad \sigma\in (-n,n)$$ was
first introduced and the flow starting from an entire Lipschitz continuous
radial graph with uniform local ball condition on the asymptotic boundary was
shown to exist for all time and converge to a complete hypersurface of constant
mean curvature with prescribed asymptotic boundary at infinity. In this paper,
we remove the uniform local ball condition on the asymptotic boundary of the
initial hypersurface, and prove that the MMCF starting from an entire locally
Lipschitz continuous radial graph exists and stays radially graphic for all
time.