Abstract.
We prove that a small analytic disc A “attached” to a pseudoconvex submanifold M of 
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 of M 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]).
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Zampieri, G. Analytic discs in pseudoconvex submanifolds of 
of higher codimension.
manuscripta math. 116, 397–400 (2005). https://doi.org/10.1007/s00229-004-0525-2
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DOI: https://doi.org/10.1007/s00229-004-0525-2