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Local Peak Sets in Weakly Pseudoconvex Boundaries in ℂ n
Borhen Halouani1
1 LMPA, Centre Universitaire de la Mi-Voix. Bât H. Poincaré, 50 rue F. Buisson, B.P. 699, F-62228 Calais Cédex, France.
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 3, pp. 577-598.

We give a sufficient condition for a C ω (resp. C ∞ )-totally real, complex-tangential, (n-1)-dimensional submanifold in a weakly pseudoconvex boundary of class C ω (resp. C ∞ ) to be a local peak set for the class 𝒪 (resp. A ∞ ). Moreover, we give a consequence of it for Catlin’s multitype.

On donne une condition suffisante pour qu’une sous variété C ω (resp. C ∞ ), totalement réelle, complexe-tangentielle, de dimension (n-1) dans le bord d’un domaine faiblement pseudoconvexe de ℂ n , soit un ensemble localement pic pour la classe 𝒪 (resp. A ∞ ). De plus, on donne une conséquence de cette condition en terme de multitype de D. Catlin.

DOI: 10.5802/afst.1215

Borhen Halouani 1

1 LMPA, Centre Universitaire de la Mi-Voix. Bât H. Poincaré, 50 rue F. Buisson, B.P. 699, F-62228 Calais Cédex, France. 
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     author = {Borhen Halouani},
     title = {Local {Peak} {Sets} in {Weakly} {Pseudoconvex} {Boundaries} in $\mathbb{C}^n$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {577--598},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
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     volume = {Ser. 6, 18},
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Borhen Halouani. Local Peak Sets in Weakly Pseudoconvex Boundaries in $\mathbb{C}^n$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 3, pp. 577-598. doi : 10.5802/afst.1215. https://afst.centre-mersenne.org/articles/10.5802/afst.1215/

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