In this paper, we show that given a set of lengths of closed geodesics, there are only finitely many convex cocompact hyperbolic 3-manifolds with that specified length spectrum with multiplicity, homotopy equivalent to a given 3-manifold without a handlebody factor, up to orientation preserving isometries.

中文翻译：

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凸协紧双曲 3 流形上的等谱有限性

在本文中，我们表明，给定一组封闭测地线的长度，只有有限多个具有指定长度谱的凸协紧双曲 3 流形，具有多重性，同伦等效于给定的 3 流形，没有手柄体因子，最多方向保持等距。