Complex analytic curves of minimal area in cubes (Q2639199)

It is proven that every complex analytic curve in a cube I of \({\mathbb{C}}^ n\) and passing through the center P of I has area not smaller than the area of the intersection of I with a complex line through P. The proof uses only real analysis methods; as a necessary step in the proof the following result is proven; let A be the union of a finite number of rectifiable (real) curves contained in the boundary of the real cube \(\{(x_ 1,...,x_ n)\in {\mathbb{R}}^ n:| x_ i| j\leq 1\) for all \(i\}\) ; assume that A intersects almost all hyperplanes in at least m points; then length (A)\(\geq 4m\).