caa a22 4500 469117389 CHVBK 20180323133128.0 cr unu---uuuuu 170328e19920701xx s 000 0 eng 10.1007/BF02934585 doi (NATIONALLICENCE)springer-10.1007/BF02934585 Iordan Andrei Analyse Complexe et Géométrie, Université Paris VI, 75252, Paris Cedex 05, France aut Maximum modulus sets in pseudoconvex boundaries [Elektronische Daten] [Andrei Iordan] LedD be a strictly pseudoconvex domain in ℂ n withC ∞ boundary. We denote byA ∞(D) the set of holomorphic functions inD that have aC ∞ extension to $$\bar D$$ . A closed subsetE of ∂D is locally a maximum modulus set forA ∞(D) if for everyp∈E there exists a neighborhoodU ofp andf∈A ∞(D∩U) such that |f|=1 onE∩U and |f|<1 on $$\bar D \cap U\backslash E$$ . A submanifoldM of ∂D is an interpolation manifold ifT p (M)⊂T p c (∂D) for everyp∈M, whereT p c (∂D) is the maximal complex subspace of the tangent spaceT p (∂D). We prove that a local maximum modulus set forA ∞ (D) is locally contained in totally realn-dimensional submanifolds of ∂D that admit a unique foliation by (n−1)-dimensional interpolation submanifolds. LetD =D 1 x ... xD r ⊂ ℂ n whereD i is a strictly pseudoconvex domain withC ∞ boundary in ℂ n i ,i=1, ,r. A submanifoldM of ∂D 1× ×∂D r verifies the cone condition if $$II_p (T_p (M)) \cap \bar C[Jn_1 (p),...,Jn_r (p)] = \{ 0\} $$ for everyp∈M, wheren i (p) is the outer normal toD i atp, J is the complex structure of ℂ n , $$\bar C[Jn_1 (p),...,Jn_r (p)]$$ is the closed positive cone of the real spaceV p generated byJ n 1(p), ,J n r(p), and II p is the orthogonal projection ofT p (∂D) onV p . We prove that a closed subsetE of ∂D 1× ×∂D r which is locally a maximum modulus set forA ∞(D) is locally contained inn-dimensional totally real submanifolds of ∂D 1× ×∂D r that admit a foliation by (n−1)-dimensional submanifolds such that each leaf verifies the cone condition at every point ofE. A characterization of the local peak subsets of ∂D 1× ×∂D r is also given. Mathematica Josephina, Inc., 1992 Complex-tangential nationallicence cone condition nationallicence interpolation manifold nationallicence maximum modulus set nationallicence peak set nationallicence pseudoconvex domain nationallicence The Journal of Geometric Analysis Springer-Verlag 2/4(1992-07-01), 327-349 1050-6926 2:4<327 1992 2 12220 https://doi.org/10.1007/BF02934585 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02934585 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Iordan Andrei Analyse Complexe et Géométrie, Université Paris VI, 75252, Paris Cedex 05, France aut NATIONALLICENCE 773 0- The Journal of Geometric Analysis Springer-Verlag 2/4(1992-07-01), 327-349 1050-6926 2:4<327 1992 2 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer