Abstract
The “counterspherical representation” of a surface in Euclidean 3-space is introduced in this paper. For meromorphic minimal surfaces in isothermal representation, the familiar spherical representation and the new counterspherical representation together give a physical interpretation of the “visibility function” that appears when the Nevanlinna theory of meromorphic functions of a complex variable is extended to these surfaces. In particular, the spherical and counterspherical representations can be used to show that the fundamental theorem of algebra for rational and logarithmico-rational minimal surfaces can be regarded not merely as an analytic theorem but also as a topological result.
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