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CR mappings and their holomorphic extension

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  • Mathematics

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CR mappings and their holomorphic extension JOURNÉES ÉQUATIONS AUX DÉRIVÉES PARTIELLES MOHAMED S. BAOUENDI LINDA P. ROTHSCHILD CR mappings and their holomorphic extension Journées Équations aux dérivées partielles (1987), p. 1-6. <http://www.numdam.org/item?id=JEDP_1987____A23_0> © Journées Équations aux dérivées partielles, 1987, tous droits réservés. L’accès aux archives de la revue « Journées Équations aux dérivées partielles » (http://www. math.sciences.univ-nantes.fr/edpa/), implique l’accord avec les conditions générales d’utili- sation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression sys- tématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi- chier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ XXI 11-1 CR MAPPINGS AND THEIR HOLOLOMORPHIC EXTENSION M. S. BAOUENDI LINDA PREISS ROTHSCHILD PURDUE UNIVERSITY UNIVERSITY OF CALIFORNIA, SAN DIEGO WEST LAFAYETTE, IN 47907 LA JOLLA, CA 92093 If M is a smooth manifold of real dimension 2n+1, we say that M is a CR manifold of codimension one with CR bundle "V, if V is a subbundle of CTM, the complexified tangent bundle of M, satisfying dimc'V= n, 'Vn'V=0. Any smooth real hypersurface M in C"'4'1 is a CR manifold of codimension one, where 'V is the subbundle of antiholomorphic tangent vectors to M. Let (M, 'V) and (M', V) be two CR manifolds of codimension one. A smooth mapping from M into M' is called CR if for all p C M H'W C V^). We recall the following definition introduced in Baouendi-Jacobowitz-Treves [3]. If M is a real analytic hypersurface in C^1 containing the origin and defined locally by p{z^~z\ = 0, dp 7^ 0, we say that M is essentially finite at 0 if for any sufficiently small z C C^^VO}, there exists an arbitrarily small $• € C^1 satisfying: p(z, ?) ^ 0, p(0, ?) = 0. Our main result is the following: THEO

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