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OverviewSince the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other. Full Product DetailsAuthor: Serge LangPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of hardcover 1st ed. 1987 Dimensions: Width: 15.50cm , Height: 1.40cm , Length: 23.50cm Weight: 0.454kg ISBN: 9781441930828ISBN 10: 1441930825 Pages: 272 Publication Date: 01 December 2010 Audience: Professional and scholarly , General/trade , Professional & Vocational , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents0 Preliminaries.- I Basic Properties.- II Hyperbolic Imbeddings.- III Brody’s Theorem.- IV Negative Curvature on Line Bundles.- V Curvature on Vector Bundles.- VI Nevanlinna Theory.- VII Applications to Holomorphic Curves in Pn.- VIII Normal Families of the Disc in Pn Minus Hyperplanes.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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