Abstract
We prove that given a family (G_t) of strictly pseudoconvex domains varying in mathcal {C}^2 topology on domains, there exists a continuously varying family of peak functions h_{t,zeta } for all G_t at every zeta in partial G_t.
Highlights
1 Introduction Let D ⊂ Cn be a bounded domain and let ζ be a boundary point of D. It is called a peak point with respect to O(D), the family of functions which are holomorphic in a neighborhood of D, if there exists a function f ∈ O(D) such that f (ζ ) = 1 and f (D\{ζ }) ⊂ D := {z ∈ C : |z| < 1}
The concept of peak functions appears to be a powerful tool in complex analysis with many applications
It is well known that every boundary point of strictly pseudoconvex domain is a peak point
Summary
Let D ⊂ Cn be a bounded domain and let ζ be a boundary point of D. It is called a peak point with respect to O(D), the family of functions which are holomorphic in a neighborhood of D, if there exists a function f ∈ O(D) such that f (ζ ) = 1 and f (D\{ζ }) ⊂ D := {z ∈ C : |z| < 1}. Such a function is a peak function for D at ζ. In [7] it is showed that, given a strictly pseudoconvex
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