Levi geometry

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The relationship between the Levi geometry of a submanifold of C” and the tangential Cauchy-Riemann equations is studied. On a real analytic codimension two submanifold of C”, we find conditions on the Levi algebra which allow us to locally solve the tangential Cauchy-Riemann equations (in most bidegrees) with kernels. Under the same conditions, we show that, locally, any CR-function is the boundary value jump of a holomorphic function defined on some suitable open set in C". This boundary value jump result is the best possible result because we also show that there is no one-sided extension theory for such submanifolds of C". In fact, we show that if S is a real analytic, generic, submanifold of C" (any codimension) where the excess dimension of the Levi algebra is less than the real codimension, then S is not extendible to any open set in C".

Original languageEnglish (US)
Pages (from-to)351-374
Number of pages24
JournalTransactions of the American Mathematical Society
Volume272
Issue number1
DOIs
StatePublished - 1982
Externally publishedYes

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Submanifolds
Algebra
Codimension
Cauchy-Riemann Equations
Geometry
Boundary Value
Open set
Jump
CR Functions
Extension Theory
Excess
Analytic function
kernel

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Levi geometry. / Boggess, Albert.

In: Transactions of the American Mathematical Society, Vol. 272, No. 1, 1982, p. 351-374.

Research output: Contribution to journalArticle

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