The geometry of total curvature on complete open surfaces

K. Shiohama, T. Shioya, M. Tanaka

294 pages, parution le 24/11/2003

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Résumé

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.

Riemannian geometry
Classical results by Cohn-Vossen and Huber
The ideal boundary
The cut loci of complete open surfaces
Isoperimetric inequalities
Mass of rays
Poles and cut loci of a surface of revolution
Behaviour of geodesics
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	K. Shiohama, T. Shioya, M. Tanaka
Parution	24/11/2003
Nb. de pages	294
Format	16 x 23,5
Couverture	Relié
Poids	530g
Intérieur	Noir et Blanc
EAN13	9780521450546
ISBN13	978-0-521-45054-6