Remarks on variational problems for Fefferman's measure
Complex Variables
2011-09-28 v1
Abstract
We investigate the Plateau and isoperimetric problems associated to Fefferman's measure for strongly pseudoconvex real hypersurfaces in (focusing on the case ), 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.
Keywords
Cite
@article{arxiv.1109.5882,
title = {Remarks on variational problems for Fefferman's measure},
author = {David E. Barrett and Christopher Hammond},
journal= {arXiv preprint arXiv:1109.5882},
year = {2011}
}