We prove that a small analytic disc A “attached” to a pseudoconvex submanifold M of CN and which shares a conormal with M at some boundary point, is in fact contained in M. The proof uses an argument of “reduction to a hypersurface” by a symplectic complex transformation. The result is classical in case codM = 1 (cf. e.g. [4]); it is a consequence of Hopf’s Lemma applied to a plurisubharmonic defining function ofM as in [5]. It was already generalized to the higher codimension in [8] but under the additional assumption, in the present paper, that A has an analytic “lift” A ∗ in T ∗ X “attached” to T ∗ MX (i.e. A has “defect” ≥ 1 in the terminology of [6], [7])
Analytic discs in pseudoconvex submanifolds of C^N of higher codimension
ZAMPIERI, GIUSEPPE
2005
Abstract
We prove that a small analytic disc A “attached” to a pseudoconvex submanifold M of CN and which shares a conormal with M at some boundary point, is in fact contained in M. The proof uses an argument of “reduction to a hypersurface” by a symplectic complex transformation. The result is classical in case codM = 1 (cf. e.g. [4]); it is a consequence of Hopf’s Lemma applied to a plurisubharmonic defining function ofM as in [5]. It was already generalized to the higher codimension in [8] but under the additional assumption, in the present paper, that A has an analytic “lift” A ∗ in T ∗ X “attached” to T ∗ MX (i.e. A has “defect” ≥ 1 in the terminology of [6], [7])Pubblicazioni consigliate
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