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Modified mean curvature flow of star-shaped hypersurfaces in hyperbolic space
2012
Communications in analysis and geometry
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We define a new version of modified mean curvature flow (MMCF) in hyperbolic space H^n+1, which interestingly turns out to be the natural negative L^2-gradient flow of the energy functional defined by De Silva and Spruck in DS09. We show the existence, uniqueness and convergence of the MMCF of complete embedded star-shaped hypersurfaces with fixed prescribed asymptotic boundary at infinity. As an application, we recover the existence and uniqueness of smooth complete hypersurfaces of constant
doi:10.4310/cag.2012.v20.n5.a6
fatcat:on6ceprp5rfrngczacoikf7uku