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SEMI LOCAL LEVI-FLAT EXTENSIONS NIKOLAY SHCHERBINA
 

Summary: SEMI LOCAL LEVI-FLAT EXTENSIONS
NIKOLAY SHCHERBINA
AND GIUSEPPE TOMASSINI
Contents
1. Introduction.
Let G be a domain in Cz Ru C2
z,w (w = u + iv). Let : b G Rv
be a continuous function and () its graph. The extendability of to
a continuous function : G Rv with the Levi-flat (i.e. foliated by
holomorphic curves) graph () has been studied by several authors
([BG], [BK], [E], [Kr], [Sh], [CS] in the case G is bounded, and [ST]
in the unbounded case) under the assumption that bG is smooth and
strictly pseudoconvex (i.e. G Rv is a strictly pseudoconvex domain
of C2
z,w). In this paper we study a semi-local version of the extension
problem, namely, when the function is prescribed on an open subset
U of bG, where bG is smooth and strictly pseudoconvex. Namely,
we define a notion of the hull E(U) G of U and prove that every
continuous function : U Rv has a Levi-flat extension to E(U).
Given an open subset D of Cn

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics