Abstract:
In this article on minimal surfaces, considered in close connection with meromorphic curves, Nevanlinna's main theorems for meromorphic functions are generalized. Besides the counting function and the characteristic function, the visibility function is introduced, which has a physical significance explained in the article and plays an essential role for minimal surfaces in $\mathbf R^n$, $n\geqslant3$, so that in this case the analog of the first main theorem is the equivisibility theorem. Moreover, an analog of Nevanlinna's second main theorem is obtained, and some properties of the characteristic function are explained that connect it with topological properties, the character of the singularities and the growth of a minimal surface.
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