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New examples of non-locally embeddable C R structures (with no non-constant C R distributions)

Jean-Pierre Rosay — 1989

Annales de l'institut Fourier

We construct examples of non-locally embeddable C R structures. These examples may show some improvement on previous examples by Nirenberg, and Jacobowitz and Trèves. They are based on a simple construction which consists in gluing two embedded structures. And (this is our main point) we believe that these examples are very transparent, therefore easy to work with.

Uniqueness in Rough Almost Complex Structures, and Differential Inequalities

Jean-Pierre Rosay — 2010

Annales de l’institut Fourier

The study of J -holomorphic maps leads to the consideration of the inequations | u z ¯ | C | u | , and | u z ¯ | ϵ | u z | . The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of u vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class 1 2 , any J -holomorphic curve that is constant on a non-empty...

Maximum modulus sets and reflection sets

Alexander NagelJean-Pierre Rosay — 1991

Annales de l'institut Fourier

We study sets in the boundary of a domain in C n , on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to , which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.

Strong boundary values : independence of the defining function and spaces of test functions

Jean-Pierre RosayEdgar Lee Stout — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.

Schwarz-type lemmas for solutions of ¯ -inequalities and complete hyperbolicity of almost complex manifolds

Sergey IvashkovichJean-Pierre Rosay — 2004

Annales de l'Institut Fourier

The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.

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