Remarks on variational problems for Fefferman's measure

Details Remarks on variational problems for Fefferman's measure Remarks on variational problems for Fefferman's measure

2011-09-27

arxiv.org/abs/1109.5882v1

Mathematics

Complex Variables

Scientific paper

We investigate the Plateau and isoperimetric problems associated to Fefferman's measure for strongly pseudoconvex real hypersurfaces in $\mathbb C^n$ (focusing on the case $n=2$), showing in particular that the isoperimetric problem shares features of both the euclidean isoperimetric problem and the corresponding problem in Blaschke's equiaffine geometry in which the key inequalities are reversed. The problems are invariant under constant-Jacobian biholomorphism, but we also introduce a non-trivial modified isoperimetric quantity invariant under general biholomorphism.

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