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Buckley, Stephen M. (2010) Nonpositive curvature and complex analysis. In: Five lectures in complex analysis : second Winter School on Complex Analysis and Operator Theory, February 5-9, 2008, University of Sevilla, Sevilla, Spain. Contemporary mathematics (525). American Mathematical Society, Providence, R.I., pp. 43-83. ISBN 9780821848098
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Abstract
We discuss a few of the metrics that are used in complex analysis and
potential theory, including the Poincaré, Carathéodory, Kobayashi, Hilbert, and quasihyperbolic
metrics. An important feature of these metrics is that they are quite often
negatively curved. We discuss what this means and when it occurs, and proceed to
investigate some notions of nonpositive curvature, beginning with constant negative
curvature (e.g. the unit disk with the Poincaré metric), and moving on to CAT(k) and
Gromov hyperbolic spaces. We pay special attention to notions of the boundary at
infinity.
| Item Type: | Book Section |
|---|---|
| Keywords: | Nonpositive curvature; complex analysis; constant negative curvature; Hyperbolic Geometry; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 2589 |
| Identification Number: | ISSN: 0271-4132 |
| Depositing User: | Prof. Stephen Buckley |
| Date Deposited: | 29 Jun 2011 13:34 |
| Publisher: | American Mathematical Society |
| Refereed: | No |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/2589 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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