In this chapter we shall show that there is a simultaneous generalization of Weyl’s Tube Formula and the Bishop-Günther Inequalities. Imagine a manifold M equipped with a family of Riemannian metrics. Intuitively, it is clear that if one varies the metric of M so that its curvature increases, then volumes in M decrease. For geodesic balls the Bishop-Günther Inequalities (Theorem 3.17, page 45) show this clearly. The situation for tubes is more complicated and interesting, however, as we shall see.
Weitere Kapitel dieses Buchs durch Wischen aufrufen
- Comparison Theorems for Tube Volumes
- Birkhäuser Basel
- Chapter 8
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