Almost monotonicity formula for H‐minimal Legendrian surfaces in the Heisenberg group

Abstract

AbstractWe prove an almost monotonicity formula for H‐minimal Legendrian Surfaces (also called contact stationary Legendrian immersions or Hamiltonian stationary immersions) in the Heisenberg Group . From this formula we deduce a Bernstein‐Liouville type theorem for H‐minimal Legendrian Surfaces. We also present some possible range of applications of this formula.