Abstract:The Asymptotic Plateau Problem asks for the existence of smooth complete hypersurfaces of constant mean curvature with prescribed asymptotic boundary at infinity in the hyperbolic space ℍ +1 . The modified mean curvature flow (MMCF)was firstly introduced by Xiao and the second author a few years back in [15], and it provides a tool using geometric flow to find such hypersurfaces with constant mean curvature in ℍ +1 . Similar to the usual mean curvature flow, the MMCF is the natural negative 2 -gradient flow of… Show more
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