Regular minimal nets on surfaces of constant negative curvature
نویسندگان
چکیده
The problem of classification of closed local minimal nets on surfaces of constant negative curvature has been formulated in [3], [4] in the context of the famous Plateau problem in the one-dimensional case. In [6] an asymptotic for log ♯(W (g)) as g → +∞ where g is genus and W (g) is the set of regular single-face closed local minimal nets on surfaces of curvature −1 has been obtained. It has been shown that ♯(W (g)) is equal to the number of classes of topological equivalence of all single-face closed local minimal nets on surfaces of curvature −1. In this paper we prove an asymptotic for ♯(W (g)) as g → +∞ and construct some examples of f -face, f > 1 nets.
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