The sub-Finsler Bernstein problem in H1

Abstract

This is a note based on the paper [32] written in collaboration with M. Ritoré. The purpose of this note is to present and discuss the Bernstein type problems in the sub-Finsler Heisenberg group H1. We give a general idea of the state of the art and we prove that a complete, stable, (X,Y)-Lipschitz surface is a vertical plane.

Keywords

• heisenberg group
• area-stationary surfaces
• sub-finsler structure
• stable surfaces
• bernstein problem
• sub-finsler perimeter