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The Geometry of Total Curvature on Complete Open Surfaces

The Geometry of Total Curvature on Complete Open Surfaces

$154.00 (C)

Part of Cambridge Tracts in Mathematics

  • Date Published: December 2003
  • availability: Available
  • format: Hardback
  • isbn: 9780521450546

$ 154.00 (C)
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About the Authors
  • This independent account of modern ideas in differential geometry shows how they can be used to understand and extend classical results in integral geometry. The authors explore the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, although their work can be extended to more general spaces. Each chapter features open problems, making the volume a suitable learning aid for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

    • Richly illustrated to aid understanding and develop intuition
    • Self-contained account requires minimal background in manifolds
    • Modern theory can extend many classical results
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    Reviews & endorsements

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

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    Product details

    • Date Published: December 2003
    • format: Hardback
    • isbn: 9780521450546
    • length: 294 pages
    • dimensions: 236 x 161 x 21 mm
    • weight: 0.535kg
    • contains: 45 b/w illus.
    • availability: Available
  • Table of Contents

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

  • Authors

    Katsuhiro Shiohama, Saga University, Japan

    Takashi Shioya, Tohoku University, Japan

    Minoru Tanaka, Tokai University, Japan

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