Modified mean curvature flow of locally Lipschitz entire radial graphs in hyperbolic space
University of California, Santa Cruz
The modified mean curvature flow (MMCF) was introduced a few years ago in my joint work with L. Xiao, where we showed the long time existence and convergence of the flow of star-shaped hypersurfaces in hyperbolic space with prescribed asymptotic boundary at infinity, assuming the so-called uniform ball condition on the boundary. In this talk, I will talk about recent joint work with P. Allmann and J. Zhu on the long-time existence of the MMCF starting from locally Lipschitz continuous entire radial graphs in hyperbolic space. This can be thought of as complement of our previous results without assuming the uniform ball condition on the boundary.