Displaying similar documents to “Analytic disks with boundaries in a maximal real submanifold of 𝐂 2 ”

Partial indices of analytic discs attached to lagrangian submanifolds of ℂ N

Josip Globevnik (1996)

Annales de l'institut Fourier

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Integers κ 1 , ... , κ N are the partial indices of an analytic disc attached to a maximally real submanifolds of ℂ N if and only if κ j ≥ 2 for at least one j . If this is the case there are a Lagrangian submanifold M of ℂ N and an analytic disc attached to M with partial indices κ 1 , ... , κ N .

Analytic regularity for the Bergman kernel

Gabor Françis, Nicholas Hanges (1998)

Journées équations aux dérivées partielles

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Let Ω ⊂ ℝ 2 be a bounded, convex and open set with real analytic boundary. Let T Ω ⊂ ℂ 2 be the tube with base Ω , and let ℬ be the Bergman kernel of T Ω . If Ω is strongly convex, then ℬ is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation, we relate the off diagonal points where analyticity fails to the Trèves curves. These curves are symplectic invariants which are determined by the CR structure of the boundary of T Ω . Note that Trèves curves...

Hulls of subsets of the torus in ℂ 2

Herbert Alexander (1998)

Annales de l'institut Fourier

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We construct a non-polynomially convex compact subset of the unit torus in ℂ 2 with polynomially convex hull containing no analytic structure.

Non-solvability of the tangential ∂̅-system in manifolds with constant Levi rank

Giuseppe Zampieri (2000)

Annales Polonici Mathematici

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Let M be a real-analytic submanifold of ℂ n whose “microlocal” Levi form has constant rank s M + + s M - in a neighborhood of a prescribed conormal. Then local non-solvability of the tangential ∂̅-system is proved for forms of degrees s M - , s M + (and 0).  This phenomenon is known in the literature as “absence of the Poincaré Lemma” and was already proved in case the Levi form is non-degenerate (i.e. s M - + s M + = n - c o d i m M ). We owe its proof to [2] and [1] in the case of a hypersurface and of a higher-codimensional submanifold...