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Hyperbolic mean curvature flow: Evolution of plane curves
In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves. More precisely, we consider a family of closed curves F : S × [0, T ) → R which satisfies the following evolution equation ∂F ∂t (u, t) = k(u, t) ~ N(u, t)− ▽ρ(u, t), ∀ (u, t) ∈ S1 × [0, T ) with the initial data F (u, 0) = F0(u) and ∂F ∂t (u, 0) = f(u) ~ N0, where k is the mean curvature an...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1973
ISSN: 0022-040X
DOI: 10.4310/jdg/1214431478