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Ideal polyhedral surfaces in Fuchsian manifolds
Geometriae Dedicata ( IF 0.5 ) Pub Date : 2019-09-07 , DOI: 10.1007/s10711-019-00480-y
Roman Prosanov

Let $$S_{g,n}$$ S g , n be a surface of genus $$g > 1$$ g > 1 with $$n>0$$ n > 0 punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an alternative proof of the existence and uniqueness of a hyperbolic polyhedral metric with prescribed curvature in a given conformal class.

中文翻译:

Fuchsian 流形中的理想多面体表面

令 $$S_{g,n}$$S g , n 是 $$g > 1$$ g > 1 的曲面,其中 $$n>0$$ n > 0 次穿刺配备完整的双曲线尖点度量。然后它可以唯一地实现为理想 Fuchsian 多面体的边界度量。在本文中,我们对这个结果给出了一个新的变分证明。我们还给出了在给定共形类中具有规定曲率的双曲多面体度量的存在性和唯一性的另一种证明。
更新日期:2019-09-07
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