Analytic regularity of CR maps into spheres

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Let M ⊂ ℂN be a connected real-analytic hypersurface and double-struck S2N′-1 ⊂ ℂN′ the unit real sphere, N′ > N ≥ 2. Assume that M does not contain any complex-analytic hypersurface of ℂN and that there exists at least one strongly pseudoconvex point on M. We show that any CR map f : M → double-struck S2N′-1 of class CN′-N+1 extends holomorphically to a neighborhood of M in ℂN.

Original languageEnglish
Pages (from-to)447-457
Number of pages11
JournalMathematical Research Letters
Issue number4
Publication statusPublished - Jul 2003
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)

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