External geometry of p-minimal surfaces

Abstract

A surface M is called p-minimal if one of the coordinate functions is p-harmonic in the inner metric. We show that in the twodimensional case the Gaussian map of such surfaces is quasiconformal. In the case when the surface is a tube we study the geometrical structure of such surfaces. In particularly, we establish the second order differential inequality for the form of the sections of M which generalizes the known ones in the minimal surfaces theory.