A new characterization of the analytic surfaces in 3 that satisfy the local Phragmén-Lindelöf condition
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Numéro Spécial : Actes du colloque Analyse Complexe et Applications en l’honneur de Nguyen Than Van, Volume 20 (2011) no. S2, pp. 71-99.

We prove that an analytic surface V in a neighborhood of the origin in 3 satisfies the local Phragmén-Lindelöf condition PL loc at the origin if and only if V satisfies the following two conditions: (1) V is nearly hyperbolic; (2) for each real simple curve γ in 3 and each d1, the (algebraic) limit variety T γ,d V satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure k-dimensional analytic variety V to satisify PL loc .

On démontre qu’une surface analytique V dans un voisinage de l’origine dans 3 satisfait à la condition Phragmén-Lindelöf locale PL loc à l’origine si et seulement si V satisfait aux deux conditions suivantes : (1) V is presque hyperbolique ; (2) pour chaque courbe réelle simple γ dans 3 et chaque d1, la variété (algebrique) limite T γ,d V satisfait à la condition de Phragmén-Lindelöf forte. Ces conditions sont aussi nécessaires que pour toute variété analytique V de dimension pure k vérifie la condition PL loc .

DOI: 10.5802/afst.1306
Braun, Rüdiger W. 1; Meise, Reinhold 2; Taylor, B. A. 3

1 Mathematisches Institut, Heinrich-Heine-Universität  Universitätsstraße 1, 40225 Düsseldorf, Germany
2 Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
3 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.
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Braun, Rüdiger W.; Meise, Reinhold; Taylor, B. A. A new characterization of the analytic surfaces in $\mathbb{C}^3$ that satisfy the local Phragmén-Lindelöf condition. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Numéro Spécial : Actes du colloque Analyse Complexe et Applications en l’honneur de Nguyen Than Van, Volume 20 (2011) no. S2, pp. 71-99. doi : 10.5802/afst.1306. http://www.numdam.org/articles/10.5802/afst.1306/

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