On minimizing surfaces of the CR invariant energy $E_1$

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.

Publication Details

Journal
ArXiv.org
Published
2025-09-30
Primary Topic
Adsorption and biosorption for pollutant removal
Type
article
Field-Weighted Citation Impact
0.00

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article

On minimizing surfaces of the CR invariant energy $E_1$

ArXiv.org
Adsorption and biosorption for pollutant removal
article

On minimizing surfaces of the CR invariant energy $E_1$

article en

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.

ArXiv.org
National Center for Theoretical Sciences, National Science and Technology Council
Affordable and clean energy
Openalex Percentile: Top 46%
Adsorption and biosorption for pollutant removal
Open Access PDFOpenAlex
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On minimizing surfaces of the CR invariant energy $E_1$ · ArXiv.org (2025) | TGRS Research Map | TGRS