On minimizing surfaces of the CR invariant energy $E_1$
Authors
Jih-Hsin Cheng
Hung-Lin Chiu
Paul Yang
Yongbing Zhang
Abstract
We study a CR-invariant equation for vanishing $E_1$ surfaces in the 3-dimensional Heisenberg group. This is shown to be a hyperbolic equation. We prove the local uniqueness theorem for an initial value problem and classify all such global surfaces with rotational symmetry. We also show that the Clifford torus in the CR 3-sphere is not a local minimizer of $E_1$ by computing the second variation.
