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  3. The Geometry of Total Curvature on Complete Open Surfaces
  • Cited by 52
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2003
Online ISBN:
9780511543159
DOI:
https://doi.org/10.1017/CBO9780511543159
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
Cambridge Tracts in Mathematics (159)
Information

Book description

This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

Reviews

'...carefully written ... a very valuable addition to libraries.'

Source: Zentralblatt MATH

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