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Proper holomorphic mappings, positivity conditions, and isometric imbedding

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Abstract

This article discusses in detail how the study of properholomorphic rational mappings between balls in differentdimensions relates to positivity conditions and to isometricimbedding of holomorphic bundles. The first chapter discussesrational proper mappings between balls; the second chapterdiscusses seven distinct positivity conditions for real-valuedpolynomials in several complex variables; the third chapterreveals how these issues relate to an isometric imbedding theoremfor holomorphic vector bundles proved by the author and Catlin.

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