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    DISCRETE SEQUENCES IN UNBOUNDED DOMAINS

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    Discrete sequences with respect to the Kobayashi distance in a strongly pseudoconvex bounded domain D are related to Carleson measures by a formula that uses the Euclidean distance from the boundary of D. Thus the speed of escape at the boundary of such sequence has been studied in details for strongly pseudoconvex bounded domain D. In this note we show that such estimations completely fail if the domain is not bounded

    Extension problems in complex and CR-geometry

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    [Excerpt from the introduction]: The aim of this thesis work is to present some of the many different extension problems that were considered in complex and CR-geometry, starting from well-known classical ones, up to the very recent still unpublished results and to the still open problems. This is going to be a (partial, since the subject is so broad) survey on the extension problems. There is neither presumption of completeness, nor a judgement on the importance of the arguments chosen, since the choice of the arguments treaten, a very personal one, simply arose from my interests of research and my mathematical experience of the last few years

    Cohomology and extension problems for semi q-coronae

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    We prove some extension theorems for analytic objects, in particular sections of a coherent sheaf, defined in semi q-coronae of a complex space. Semi q-coronae are domains whose boundary is the union of a Levi flat part, a q-pseudoconvex part and a q-pseudoconcave part. Such results are obtained mainly using cohomological techniques
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