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Kohn–rossi cohomology and its application to the complex plateau problem, iii

Rong Du East China Normal University Stephen Yau Tsinghua University

Differential Geometry mathscidoc:1609.10251

Journal of Differential Geometry, 90, (2), 251-266, 2012
Let X be a compact connected strongly pseudoconvex CR manifold of real dimension 2n . 1 in CN. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For n  3 and N = n+1, Yau found a necessary and sufficient condition for the interior regularity of the HarveyLawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For n = 2 and N  n + 1, the problem has been open for over 30 years. In this paper we introduce a new CR invariant g(1,1)(X) of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. In the case n = 2 and N = 3, the vanishing of this invariant is enough to give the interior regularity.
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@inproceedings{rong2012kohn–rossi,
  title={KOHN–ROSSI COHOMOLOGY AND ITS APPLICATION TO THE COMPLEX PLATEAU PROBLEM, III},
  author={Rong Du, and Stephen Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913223443142305913},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={2},
  pages={251-266},
  year={2012},
}
Rong Du, and Stephen Yau. KOHN–ROSSI COHOMOLOGY AND ITS APPLICATION TO THE COMPLEX PLATEAU PROBLEM, III. 2012. Vol. 90. In Journal of Differential Geometry. pp.251-266. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913223443142305913.
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