External geometry of p-minimal surfaces

TL;DR

This paper investigates the properties of p-minimal surfaces, showing that their Gaussian map is quasiconformal in two dimensions and analyzing their structure, especially for tubular surfaces, with new differential inequalities derived.

Contribution

It introduces the concept of p-minimal surfaces, proves quasiconformality of their Gaussian map in 2D, and establishes new differential inequalities for their sections.

Findings

Gaussian map of 2D p-minimal surfaces is quasiconformal

Structural analysis of tubular p-minimal surfaces

New second order differential inequalities for surface sections

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.