Local Peak Sets in Weakly Pseudoconvex Boundaries in n
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 3, p. 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 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.

@article{AFST_2009_6_18_3_577_0,
     author = {Halouani, Borhen},
     title = {Local Peak Sets in Weakly Pseudoconvex Boundaries in $\mathbb{C}^n$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 18},
     number = {3},
     year = {2009},
     pages = {577-598},
     doi = {10.5802/afst.1215},
     mrnumber = {2582442},
     zbl = {1194.32020},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2009_6_18_3_577_0}
}
Halouani, Borhen. 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. http://www.numdam.org/item/AFST_2009_6_18_3_577_0/

[B-I] Boutet de Monvel ( L.), Iordan (A.).— Peak curves in weakly Pseudoconvex Boundaries in 2 . J. Diff. Geometry 7, Number 1, p. 1-15 (1997). | MR 1630765 | Zbl 0916.32014

[Bo] Boggess (A.).— CR manifolds and the tangential Cauchy-Riemann complex. Studies in advanced mathematics (Texas A&M University) (1992). | MR 1211412 | Zbl 0760.32001

[B-S] Boas ( H.P.), Straube (E.J.).— On equality of line type and variety type of real hypersurfaces in n . J. Geom. Anal. 2, No.2, p. 95-98 (1992). | MR 1151753 | Zbl 0749.32009

[Ca] Catlin (D.).— Boundary invariants of pseudoconvex domains. Annals of Mathematics, 120, p. 529-586 (1984). | MR 769163 | Zbl 0583.32048

[DA] D’Angelo (J.P.).— Real hypersurfaces, orders of contact, and applications. Annals of Mathematics, 115, p. 615-637 (1982). | MR 657241 | Zbl 0488.32008

[H-S] Hakim (M.), Sibony (N.).— Ensembles pics dans les domaines strictement pseudoconvexes. Duke Math. J. 45, p. 601-607 (1978). | MR 507460 | Zbl 0402.32008

[Mi] Michel (J.).— Integral representations on weakly pseudoconvex domains. Math. Z. 208, No. 3, p. 437-462 (1991). | MR 1134587 | Zbl 0725.32002

[Na] Narasimhan (R.).— Analysis on Real and Complex Manifolds. North-Holland Mathematical Library (1968) | MR 251745 | Zbl 0188.25803