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
URI:	http://www.ams.org/journals/
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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