Geometric conditions which imply compactness of the $\overline{\partial }$-Neumann operator

Straube, Emil

Annales de l'Institut Fourier, Tome 54 (2004) no. 3, pp. 699-710.

On donne, pour les domaines lisses bornés pseudoconvexes de ${ℂ}^2$, des conditions géométriques concernant le bord qui entraînent la compacité de l’opérateur $\overline{\partial }$-Neumann. Il est remarquable que la preuve de la compacité ne procède pas par verification des conditions suffisantes bien connues de type théorie du potentiel.

For smooth bounded pseudoconvex domains in ${ℂ}^2$, we provide geometric conditions on the boundary which imply compactness of the $\overline{\partial }$-Neumann operator. It is noteworthy that the proof of compactness does not proceed via verifying the known potential theoretic sufficient conditions.

Classification : 32W05
Keywords: $\overline{\partial }$-Neumann operator, compactness, geometric conditions
Mot clés : opérateur $\overline{\partial }$-Neumann, compacité, conditions géométriques

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