Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips

TL;DR

This paper establishes a monotonicity property of the horizontal perimeter at specific points for certain surfaces within the Heisenberg group, advancing understanding of geometric measure theory in sub-Riemannian spaces.

Contribution

It introduces a new monotonicity result for the horizontal perimeter of graphical strips in the Heisenberg group, expanding the theoretical framework of sub-Riemannian calculus.

Findings

Monotonicity of horizontal perimeter proved at specific points.

Applicable to a class of surfaces called graphical strips.

Enhances understanding of geometric properties in the Heisenberg group.

Abstract

We prove a monotonicity result at specific points for the Horizontal Perimeter for a class of surfaces in the Heisenberg group.