Convex domains of finite type.

*(English)*Zbl 0777.31007Let \(\Omega\subset\subset\mathbb{C}^ n\) be a smoothly bounded domain and \(p\in\partial\Omega\). Let \(p\) have a neighbourhood \(U\) in which \(\Omega\) is convex. Suppose that the line type of \(p\) is \(L<\infty\). The author proves that for each \(z\in\Omega\cap U\), there exists a uniformly bounded \(C^ \infty\)-plurisubharmonic function on \(\Omega\) with maximally large Hessian on a polydisc \(P_ \delta(z)\). As a consequence, it is deduced that the variety type of \(p\) is also finite and equals \(L\). This corollary is also known to Fornaess-Sibony and Boas-Straube by different methods.

Reviewer: V.Anandam (Riyadh)

##### MSC:

31C10 | Pluriharmonic and plurisubharmonic functions |

32A10 | Holomorphic functions of several complex variables |

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\textit{J. D. McNeal}, J. Funct. Anal. 108, No. 2, 361--373 (1992; Zbl 0777.31007)

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##### References:

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