External geometry of p-minimal surfaces

Details External geometry of p-minimal surfaces External geometry of p-minimal surfaces

2009-03-01

arxiv.org/abs/0903.0176v1

Geometry from the Pacific Rim (Singapore, 1994), de Gruyter, Berlin, 1997, 363-375

Mathematics

Differential Geometry

Scientific paper

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.

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