000			02687nam a22003978i 4500
001			CR9780511543159
003			UkCbUP
005			20200124160239.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2003||||enk o ||1 0|eng|d
020			_a9780511543159 (ebook)
020			_z9780521450546 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA670 _b.S48 2003
082	0	0	_a516.3/52 _221
100	1		_aShiohama, K. _q(Katsuhiro), _d1940- _eauthor.
245	1	4	_aThe geometry of total curvature on complete open surfaces / _cKatsuhiro Shiohama, Takashi Shioya, Minoru Tanaka.
264		1	_aCambridge : _bCambridge University Press, _c2003.
300			_a1 online resource (ix, 284 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v159
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_a1. 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			_aThis 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	_aRiemannian manifolds.
650		0	_aCurves on surfaces.
650		0	_aGlobal differential geometry.
700	1		_aShioya, Takashi, _d1963- _eauthor.
700	1		_aTanaka, Minoru, _d1949- _eauthor.
776	0	8	_iPrint version: _z9780521450546
830		0	_aCambridge tracts in mathematics ; _v159.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543159
999			_c518320 _d518318