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On résout à l’aide de formules intégrales explicites les équations de Cauchy-Riemann sur le triangle de Hartogs. On montre que, si la donnée est dans une classe höldérienne $C^{p, α}$ , la solution est dans la même classe.

Regularity and extremality of quasiconformal homeomorphisms on CR 3-manifolds.

Tang, Puqi (1996)

Annales Academiae Scientiarum Fennicae. Mathematica

Regularity of local embeddings of strictly pseudoconvex CR structures.

Joachim Michel, Lan Ma (1994)

Journal für die reine und angewandte Mathematik

Regularity of the Bergman Projection in Weakly Pseudoconvex Domains.

Steven R. Bell, Harold P. Boas (1981)

Mathematische Annalen

Regularity of the Bergman Projection on Domains with Partial Transverse Symmetries.

So-Chin Chen (1987)

Mathematische Annalen

Regularity of the $\bar{\partial}$ -Neumann problem

J. J. Kohn (1980/1981)

Séminaire Équations aux dérivées partielles (Polytechnique)

Regularity of varieties in strictly pseudoconvex domains.

Franc Forstneric (1988)

Publicacions Matemàtiques

We prove a theorem on the boundary regularity of a purely p-dimensional complex subvariety of a relatively compact, strictly pseudoconvex domain in a Stein manifold. Some applications describing the structure of the polynomial hull of closed curves in Cn are also given.

Residues, currents, and their relation to ideals of holomorphic functions.

Mikael Passare (1988)

Mathematica Scandinavica

Résultats d'unicité de Cauchy instable dans des situations où la condition de pseudo-convexité dégénère

Xavier Saint Raymond (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Riemann maps in almost complex manifolds

Bernard Coupet, Hervé Gaussier, Alexandre Sukhov (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.

Riemann-Roch Theorem for Strongly Pseudoconvex Manifolds of Dimension 2.

Masahide Kato (1976)

Mathematische Annalen

Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Stephen S.-T. Yau (2011)

Journal of the European Mathematical Society

Let $X_{1}$ and $X_{2}$ be two compact strongly pseudoconvex CR manifolds of dimension $2 n - 1 \geq 5$ which bound complex varieties $V_{1}$ and $V_{2}$ with only isolated normal singularities in $ℂ^{N 1}$ and $ℂ^{N 2}$ respectively. Let $S_{1}$ and $S_{2}$ be the singular sets of $V_{1}$ and $V_{2}$ respectively and $S_{2}$ is nonempty. If $2 n - N_{2} - 1 \geq 1$ and the cardinality of $S_{1}$ is less than 2 times the cardinality of $S_{2}$ , then we prove that any non-constant CR morphism from $X_{1}$ to $X_{2}$ is necessarily a CR biholomorphism. On the other hand, let $X$ be a compact strongly pseudoconvex CR manifold of...

Rigidity of CR submanifolds and analyticity of CR immersions.

Chong-Kyu Han (1990)

Mathematische Annalen

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