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Maximum Modulus Sets and Segre Convexity
Author(s) -
Cœuré Gérard,
Honvault Pascal
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200110)230:1<37::aid-mana37>3.0.co;2-l
Subject(s) - codimension , mathematics , convexity , boundary (topology) , analytic function , manifold (fluid mechanics) , mathematical analysis , pure mathematics , interpolation (computer graphics) , modulus , domain (mathematical analysis) , function (biology) , regular polygon , convex function , combinatorics , geometry , physics , motion (physics) , mechanical engineering , financial economics , engineering , economics , classical mechanics , evolutionary biology , biology
Let E be a totally real, analytic, n ‐dimensional manifold, foliated by analytic interpolation submanifolds of codimension 1, in the analytic boundary of a Segre‐convex domain in ℂ n . Given a canonical defining function of the boundary of Ω in a point 0 of E : Im z 1 + R [Re z 1 , z ′, z̄′]=0. If all the odd exponents in the decomposition of R in irreducible factors, at 0,are greater than 1 then R ≥0 and E is locally contained in a maximum modulus set.