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 ℝ n +1 ( n ⩾ 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 ℝ 2 , whose evolving curves move normally.

中文翻译：

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双曲反平均曲率流

在假设 ℝ n +1 ( n ⩾ 2) 的初始紧致光滑超曲面是平均凸面和星形的假设下，我们证明了双曲反（平均）曲率流（有或没有指定的强迫项）的短期存在性成形。显示了几个有趣的例子和一些演化超曲面几何量的双曲线演化方程。此外，在不同的初速度假设下，我们可以得到平面ℝ 2 中的双曲反平均曲率流的展开和收敛结果，其演化曲线正常移动。