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Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity

Christine Laurent-Thiébaut, Egmon Porten (2003)

Annales de l’institut Fourier

Let D n , n 2 , be a domain with C 2 -boundary and K D be a compact set such that D K is connected. We study univalent analytic extension of CR-functions from D K to parts of D . Call K CR-convex if its A ( D ) -convex hull, A ( D ) - hull ( K ) , satisfies K = D A ( D ) - hull ( K ) ( A ( D ) denoting the space of functions, which are holomorphic on D and continuous up to D ). The main theorem of the paper gives analytic extension to D A ( D ) - hull ( K ) , if K is CR- convex.

Analytic inversion of adjunction: L 2 extension theorems with gain

Jeffery D. McNeal, Dror Varolin (2007)

Annales de l’institut Fourier

We establish new results on weighted L 2 -extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold.

Analytic regularity for the Bergman kernel

Gabor Françis, Nicholas Hanges (1998)

Journées équations aux dérivées partielles

Let Ω 2 be a bounded, convex and open set with real analytic boundary. Let T Ω 2 be the tube with base Ω , and let be the Bergman kernel of T Ω . If Ω is strongly convex, then 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 exist only...

Analytic rings

Eduardo Dubuc, Gabriel Taubin (1983)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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