Displaying similar documents to “On the hull of holomorphy of an n -manifold in C n ”

Analytic disks with boundaries in a maximal real submanifold of 𝐂 2

Franc Forstneric (1987)

Annales de l'institut Fourier

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Let M be a two dimensional totally real submanifold of class C 2 in C 2 . A continuous map F : Δ ‾ → C 2 of the closed unit disk Δ ‾ ⊂ C into C 2 that is holomorphic on the open disk Δ and maps its boundary b Δ into M is called an analytic disk with boundary in M . Given an initial immersed analytic disk F 0 with boundary in M , we describe the existence and behavior of analytic disks near F 0 with boundaries in small perturbations of M in terms of the homology class of the closed curve F 0 ( b Δ ) in M . We also prove a regularity...

Embeddability of abstract CR structures and integrability of related systems

Salah Baouendi, Linda P. Rothschild (1987)

Annales de l'institut Fourier

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Necessary and sufficient conditions for local embeddability of abstract C R structures are expressed in terms of the commutation of the C R vector fields with a complex Lie algebra. These results extend to more general systems.

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 .

On the existence of canard solutions

Daniel Panazzolo (2000)

Publicacions Matemàtiques

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We study the existence of global canard surfaces for a wide class of real singular perturbation problems. These surfaces define families of solutions which remain near the slow curve as the singular parameter goes to zero.

Maximum modulus sets

Thomas Duchamp, Edgar Lee Stout (1981)

Annales de l'institut Fourier

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We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain D of dimension N . If Σ ⊂ b D is a smooth manifold of dimension N and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in A 2 ( D ) with the same smooth N -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in H 1 ( D , R ) vanishes or...