A Free Boundary Isoperimetric Problem in the Hyperbolic Space between parallel horospheres

Details A Free Boundary Isoperimetric Problem in the Hyperbolic Space between parallel horospheres A Free Boundary Isoperimetric Problem in the Hyperbolic Space between parallel horospheres

2008-11-06

arxiv.org/abs/0811.1046v1

Mathematics

Differential Geometry

Scientific paper

In this work we investigate the following isoperimetric problem: to find the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the area of the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behaviour of the profile curves of the rotational surfaces with constant mean curvature in the hyperbolic space.

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