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Bryant Surfaces

​
μ
0.4
l
2
b
0.5
d
1
x
6.283
y
3.141
warped
A Bryant surface (or catenoid cousin) is a two-dimensional surface embedded in three-dimensional hyperbolic space with constant mean curvature equal to 1. Bryant derived a holomorphic parameterization for such surfaces, similar to the Weierstrass–Enneper parameterization for minimal surfaces [1, 2].
A one-parameter family of these surfaces of revolution is defined for the parameter
μ
; for
-1/2<μ<0
​
the surface is embedded, and for
μ>0
the surface is not embedded; as
μ
tends to zero, the surfaces converge to two horospheres [3, 4, 5]. Another family that arises consists of warped surfaces that are not surfaces of revolution with two regular embedded ends, with
l
warps and parameters
b
and
d
[6, 7]. The parameters
x
and
y
control the range over which the surface is plotted.
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