The paper studies a newly discovered family of one-parameter even-dimensional
linear transformations with geometric properties revealing local variational
characterization of embedded minimal surfaces in three-dimensional Euclidean
space. It is also explicitly shown that these properties are responsible for
the existence of only two possible fundamental local models for any embedded
minimal surface in n three-dimensional Euclidean space, namely, the helicoid
and the catenoid. A new term Lebesgue measure dissipation is introduced and
locally characterizes the geometry of the positive area increment for all
embedded surfaces which are not minimal.