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Variational Problems for Fefferman Hypersurface Measure and Volume-Preserving CR Invariants

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Abstract

We derive Euler’s equation for the isoperimetric problem and the extremal hypersurface problem associated with Fefferman hypersurface measure for strongly pseudoconvex real hypersurfaces in ℂ2. We use volume-preserving CR invariants to show that the only “torsion-free” solutions of Euler’s equation for the isoperimetric problem are the volume-preserving images of spheres.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Christopher Hammond

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  1. Christopher Hammond
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Correspondence to Christopher Hammond.

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Communicated by Alexander Isaev.

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Hammond, C. Variational Problems for Fefferman Hypersurface Measure and Volume-Preserving CR Invariants. J Geom Anal 21, 372–408 (2011). https://doi.org/10.1007/s12220-010-9151-2

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  • DOI: https://doi.org/10.1007/s12220-010-9151-2

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