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Analysis on Manifolds and the Ricci Curvature

  • Sylvestre Gallot
  • Dominique Hulin
  • Jacques Lafontaine
Chapter
  • 414 Downloads
Part of the Universitext book series (UTX)

Abstract

Even though we are mainly concerned with the so called closed manifolds, it is necessary to introduce manifolds with boundary. On one hand, we cannot ignore mathematical beings which locally behave like domains on R n , just as manifolds locally behave like R n . On the other hand, when doing Analysis on manifolds, it may useful to cut them into small pieces (cf. for example 4.65 and 4.68 below). These pieces are no more manifolds, but they will be manifolds with boundary.

Keywords

Riemannian Manifold Differential Operator Neumann Problem Ricci Curvature Compact Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 2
  • Jacques Lafontaine
    • 3
  1. 1.Université de SavoieChambéry CedexFrance
  2. 2.Centre d’Orsay, MathématiqueUniversité Paris11Orsay CedexFrance
  3. 3.U.F.R. de MathématiquesUniversité Paris 7Paris Cedex 05France

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