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Keywords:
evolution equation; hyperbolic inverse mean curvature flow; short time existence
evolution equation; hyperbolic inverse mean curvature flow; short time existence
Summary:
We prove the short-time existence of the hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb {R}^{n+1}$ ($n\ge 2$) is mean convex and star-shaped. Several interesting examples and some hyperbolic evolution equations for geometric quantities of the evolving hypersurfaces are shown. Besides, under different assumptions for the initial velocity, we can get the expansion and the convergence results of a hyperbolic inverse mean curvature flow in the plane $\mathbb {R}^2$, whose evolving curves move normally.
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