On minimizing surfaces of the CR invariant energy E1
Abstract
We study a CR-invariant equation for vanishing E1 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 E1 by computing the second variation.
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