Analysis on Manifolds and the Ricci Curvature
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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.
KeywordsRiemannian Manifold Differential Operator Neumann Problem Ricci Curvature Compact Riemannian Manifold
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