Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups $H^n, n>1$

TL;DR

This paper proves that Lipschitz intrinsic graphs in higher-dimensional Heisenberg groups that solve the minimal surface equation via vanishing viscosity are actually smooth, revealing regularity properties in sub-Riemannian geometry.

Contribution

It establishes the smoothness of Lipschitz solutions to the minimal surface equation in Heisenberg groups for dimensions greater than one, extending regularity results in sub-Riemannian geometry.

Findings

Lipschitz intrinsic graphs are smooth if they are vanishing viscosity solutions.

Regularity results hold specifically for Heisenberg groups with n>1.

The minimal surface equation solutions exhibit higher regularity than previously known.

Abstract

We prove that Lipschitz intrinsic graphs in the Heisenberg groups $H^n$, with $n>1$, which are vanishing viscosity solutions of the minimal surface equation are smooth.