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The geometry of total curvature on complete open surfaces /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The geometry of total curvature on complete open surfaces // Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka.
Author:	Shiohama, K.
other author:	Shioya, Takashi,
Description:	1 online resource (ix, 284 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Riemannian manifolds. -
Online resource:	https://doi.org/10.1017/CBO9780511543159
ISBN:	9780511543159 (ebook)

The geometry of total curvature on complete open surfaces /
Shiohama, K.1940-

The geometry of total curvature on complete open surfaces /Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka. - 1 online resource (ix, 284 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;159. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics.

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.

ISBN: 9780511543159 (ebook)Subjects--Topical Terms:

580421
Riemannian manifolds.

LC Class. No.: QA670 / .S48 2003

Dewey Class. No.: 516.3/52

The geometry of total curvature on complete open surfaces /
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100 1 $a Shiohama, K. $q (Katsuhiro), $d 1940- $e author. $3 1440982
245 1 4 $a The geometry of total curvature on complete open surfaces / $c Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka.
264 1 $a Cambridge : $b Cambridge University Press, $c 2003.
300 $a 1 online resource (ix, 284 pages) : $b digital, PDF file(s).
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490 1 $a Cambridge tracts in mathematics ; $v 159
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics.
520 $a 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.
650 0 $a Riemannian manifolds. $3 580421
650 0 $a Curves on surfaces. $3 893597
650 0 $a Global differential geometry. $3 672282
700 1 $a Shioya, Takashi, $d 1963- $e author. $3 1440983
700 1 $a Tanaka, Minoru, $d 1949- $e author. $3 1440984
776 0 8 $i Print version: $z 9780521450546
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511543159