Displaying similar documents to “Local Boundary Regularity of the Canonical Einstein-Kähler Metric on Pseudoconvex Domains.”

∂̅-cohomology and geometry of the boundary of pseudoconvex domains

Takeo Ohsawa (2007)

Annales Polonici Mathematici

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In 1958, H. Grauert proved: If D is a strongly pseudoconvex domain in a complex manifold, then D is holomorphically convex. In contrast, various cases occur if the Levi form of the boundary of D is everywhere zero, i.e. if ∂D is Levi flat. A review is given of the results on the domains with Levi flat boundaries in recent decades. Related results on the domains with divisorial boundaries and generically strongly pseudoconvex domains are also presented. As for the methods, it is explained...

On isometries of the Kobayashi and Carathéodory metrics

Prachi Mahajan (2012)

Annales Polonici Mathematici

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This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between...