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LEVI FLATNESS AND STEIN BASIS DELLA SALA AND GIUSEPPE TOMASSINI
 

Summary: LEVI FLATNESS AND STEIN BASIS
DELLA SALA AND GIUSEPPE TOMASSINI
1. Introduction
Let be a bounded domain in Cn
with smooth boundary and M
a topological (2n-1)-dimensional hypersurface of , with boundary
bM b. M is said to be Levi flat if its interior is foliated by complex
hypersurfaces (of complex dimension n-1). The question whether or
not M has a Stein basis (i.e. a fundamental system of Stein neighbour-
hoods) is natural. We formulate the following conjecture:
( ) if is strongly pseudoconvex and bM is a topological (2n - 1)-
sphere, then M has a Stein basis.
In this paper we discuss this problem assuming that is a strongly
pseudoconvex domain in C2
.
More generally, we consider a topological surface S b defined as
zero set {g = 0} of a continuous function g : b R and we assume,
for simplicity, that b S has two connected components S+, S- and
G has two peak points p S+, q S-, with g(p) > 0, g(q) < 0. Let
L(u) be the Levi operator introduced in [ST] and F = Fg be the family

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics